This paper investigates the problem of shared resource allocation, where a set of agents must be assigned to heterogeneous resources, with each agent allocated exactly one resource and each resource potentially shared by multiple agents. An agent’s utility for a given resource is jointly determined by the resource's type and the number of agents sharing it. We focus on two fundamental classes of monotone valuations: monotone nondecreasing and monotone nonincreasing, where an agent’s utility respectively increases or decreases with the number of agents sharing the resource. Within this shared resource framework, we examine classical notions of fairness and stability, including maximin-share fairness, envy-freeness, Nash stability, and two epistemic relaxations—epistemic envy-freeness and epistemic Nash stability—as well as swap stability. We propose formal definitions adapted to this setting and systematically analyze the relationships among these concepts. The primary contributions of this work consist of establishing existence and computational complexity results for each notion under both monotonicity assumptions and developing polynomial-time algorithms in cases where fair or stable allocations are guaranteed to exist.

We study the fair allocation of indivisible items to groups of agents from the perspectives of both the agents and a centralized allocator. In our setting, the centralized allocator aims to ensure that the allocation is fair both among the groups and between individual agents. This setting applies to many real-world scenarios, such as when a school administrator allocates resources (e.g., office spaces and supplies) to staff members within departments or when a city council allocates limited housing units to families in need across different communities. To ensure fairness between agents, we consider the classical notion of envy-freeness (EF). To ensure fairness among groups, we introduce the notion of centralized group equitability (CGEQ), which captures fairness for groups from the centralized allocator’s perspective. Because an EF or CGEQ allocation does not always exist in general, we consider their natural relaxations: envy-freeness to one item (EF1) and centralized group equitability up to one item (CGEQ1). For different classes of valuation functions of the agents and the centralized allocator, we show that allocations satisfying both EF1 and CGEQ1 always exist, and we design efficient algorithms to compute such allocations. We also consider the centralized group maximin share (CGMMS) from the centralized allocator's perspective as a group-level fairness objective with EF1 for agents, and present several results.

Urban Network Security Games (UNSGs), which model the strategic allocation of limited security resources on city road networks, are critical for urban safety. However, finding a Nash Equilibrium (NE) in large-scale UNSGs is challenging due to their massive and combinatorial action spaces. One common approach to addressing these games is the Policy-Space Response Oracle (PSRO) framework, which requires computing best responses (BR) at each iteration. However, precisely computing exact BRs is impractical in large-scale games, and employing reinforcement learning to approximate BRs inevitably introduces errors that limit the overall effectiveness of the PSRO methods. Recent advancements in leveraging non-convex stochastic optimization to approximate an NE offer a promising alternative to the burdensome BR computation. However, utilizing existing stochastic optimization techniques with an unbiased loss function for UNSGs remains challenging because the action spaces are too vast to be effectively represented by neural networks. To address these issues, we introduce Tree-based Stochastic Optimization (TSO), a framework that bridges the gap between the stochastic optimization paradigm for NE-finding and the demands of UNSGs. Specifically, we employ the tree-based action representation that maps the whole action space onto a tree structure, addressing the challenge faced by neural networks in representing actions when the action space cannot be enumerated. We then incorporate this representation into the loss function and theoretically demonstrate its equivalence to the unbiased loss function. To further enhance the quality of the converged solution, we introduce a sample-and-prune mechanism that reduces the risk of being trapped in suboptimal local optima. Extensive experimental results indicate the superiority of TSO over other baseline algorithms in addressing the UNSGs.

This paper studies a scheduling problem with machine calibrations for multi-interval jobs. More exactly, there are n (possibly weighted) jobs of unit size that must be scheduled on a single initially uncalibrated machine. The machine can process jobs only when calibrated, and such a calibration lasts for T time slots. The standard model by Bender et al. [Bender MA, Bunde DP, Leung VJ, McCauley S, Phillips CA (2013) Efficient scheduling to minimize calibrations. Blelloch GE, Vöcking B, eds. 25th ACM Sympos. Parallelism Algorithms Architectures SPAA ‘13 (ACM, New York), 280–287] assumes that each job has a release time and deadline between which it must be processed. We study a generalization in which each job must be processed during one of possibly many job-dependent time intervals. We consider two objectives: In the minimization version, our goal is to minimize the number of calibrations while scheduling all jobs. In the maximization version, our goal is to maximize the total weight of scheduled jobs while using at most B calibrations. For the minimization version, we present a logarithmic approximation algorithm. We also prove that the problem is set-cover hard, implying that our algorithm is optimal up to a constant factor unless P = NP. The special case when each job may be scheduled in at most two time slots is shown to be vertex-cover hard, implying that there is no [Formula: see text]-approximation algorithm based on the unique game conjecture. For the maximization version, we give an algorithm with approximation ratio [Formula: see text]. This improves upon the previously best-known algorithm, which has an approximation ratio of 1/3 [Chau V, Feng S, Li M, Wang Y, Zhang G, Zhang Y (2019) Weighted throughput maximization with calibrations. Friggstad Z, Sack JR, Salavatipour MR, eds. Algorithms Data Structures 16th Internat. Sympos. WADS 2019 Proc., Lecture Notes in Computer Science, vol. 11646 (Springer, New York), 311–324]. Moreover, we also prove that our bound on the approximation ratio is tight. Although all hardness results mentioned above hold for any [Formula: see text], we provide optimal polynomial-time algorithms for T = 2 in both the minimization version and the maximization version. Finally, we show that our methods can be extended into the m identical machines case by losing some running time, whereas all algorithmic results remain the same in both versions. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.0430 .

We consider a general non-stochastic online pricing bandit setting in a procurement scenario where a buyer with a budget wants to procure items from a fixed set of sellers to maximize the buyer's reward by dynamically offering purchasing prices to the sellers, where the sellers' costs and values at each time period can change arbitrarily and the sellers determine whether to accept the offered prices to sell the items. This setting models online pricing scenarios of procuring resources or services in multi-agent systems. We first consider the offline setting when sellers' costs and values are known in advance and investigate the best fixed-price policy in hindsight. We show that it has a tight approximation guarantee with respect to the offline optimal solutions. In the general online setting, we propose an online pricing policy, Granularity-based Pricing (GAP), which exploits underlying side-information from the feedback graph when the budget is given as the input. We show that GAP achieves an upper bound of O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln B) on the alpha-regret where n, v_{max}, c_{min}, and B are the number, the maximum value, the minimum cost of sellers, and the budget, respectively. We then extend it to the unknown budget case by developing a variant of GAP, namely Doubling-GAP, and show its alpha-regret is at most O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln2 B). We also provide an alpha-regret lower bound Omega(v_{max}sqrt{Bn/c_{min}}) of any online policy that is tight up to sub-linear terms. We conduct simulation experiments to show that the proposed policy outperforms the baseline algorithms.

We study the k-facility location games with optional preferences on the line. In the games, each strategic agent has a public location preference on the k facility locations and a private optional preference on the preferred/acceptable set of facilities out of the k facilities. Our goal is to design strategyproof mechanisms to elicit agents’ optional preferences and locate k facilities to minimize the social or maximum cost of agents based on their facility preferences and public agent locations. We consider two variants of the facility location games with optional preferences: the Min variant and the Max variant where the agent’s cost is defined as their distance to the closest acceptable facility and the farthest acceptable facility, respectively. For the Min variant, we present two deterministic strategyproof mechanisms to minimize the maximum cost and social cost with k ≥ 3 facilities, achieving approximation ratios of 3 and 2n+1 respectively. We complement the results by establishing lower bounds of 3/2 and n/4 for the approximation ratios achievable by any deterministic strategyproof mechanisms for the maximum cost and social cost, respectively. We then improve our results in a special setting of the Min variant where there are exactly three facilities and present two deterministic strategyproof mechanisms to minimize the maximum cost and social cost. For the Max variant, we present an optimal deterministic strategyproof mechanism for the maximum cost and a k-approximation deterministic strategyproof mechanism for the social cost.

We consider the k-facility location problems with capacity constraints in bounded location space from the mechanism design perspective. In this problem, we seek to locate k capacity constrained facilities in a bounded interval (i.e., B=[bl,br]) to serve agents, who have preferences on the ideal locations of the facilities in the interval. Our goal is to design strategyproof mechanisms to elicit agents’ true ideal locations and locate facilities that minimize the social cost and maximum cost, which are defined to be the sum and the maximum of the agents’ costs (i.e., agents’ distances to their facilities), respectively. For the equal capacity setting without spare capacity (i.e., all the agents can be served exactly), we provide a deterministic strategyproof mechanism. For any bounded interval (i.e., bl, br∈R), our mechanism has approximation ratios of n-1 for the social cost and 4 for the maximum cost with k≥3 facilities and n≥3 agents. We also establish lower bounds of n/2 for the social cost by a common class of deterministic mechanisms that order agents from left to right, and 2 for the maximum cost by any deterministic mechanism. Our mechanism also achieves tight bounds for both costs with k<3 facilities. We then consider the equal capacity setting with spare capacity and the arbitrary capacity setting without spare capacity. For these two settings and any bounded interval, we provide randomized strategyproof mechanisms with approximation ratios of n/2 for the social cost and 2 for the maximum cost with any number of facilities. We complement this result by establishing lower bounds of 5/3 for the social cost and 3/2 for the maximum cost.

In this paper, we study a fair resource scheduling problem involving the assignment of a set of interval jobs among a group of heterogeneous machines. Each job is associated with a release time, a deadline, and a processing time. A machine can process a job if the entire processing period falls within the release time and deadline of the job. Each machine can process at most one job at any given time, and different jobs yield different utilities for the machines. The goal is to find a fair and efficient schedule of the jobs. We discuss the compatibility between envy-freeness up to any item (EFX) and various efficiency concepts. Additionally, we present polynomial-time algorithms for various settings.

Contrastive self-supervised learning has emerged as a powerful paradigm for extracting meaningful representations without labels. While effective at capturing broad categorical distinctions, current methods often struggle to preserve the fine-grained and hierarchical relationships inherent in real-world data. From the perspective of semantic alignment, conventional contrastive learning aligns representations to semantic structure at a global level, treating the entire embedding space uniformly and frequently overlooking rich local structural information. In this paper, we propose \emph{Adaptive Multi-scale Affinity alignment (AMA-alignment)}, a framework that introduces localized contrastive objectives and a dynamic multi-scale optimization strategy to adaptively identify and refine poorly aligned regions within the embedding space. Although our model is inherently more complex due to its \emph{multi-scale} and \emph{adaptive} design, we provide the theoretical guarantees indicating that its convergence rate remains comparable to that of standard smooth non-convex optimization. We conduct a set of experiments on diverse benchmarks to show that AMA-alignment can effectively preserve hierarchical structure; moreover, AMA-alignment also outperforms existing contrastive methods on a range of downstream tasks.

Deep learning models often struggle with distribution shifts between training and deployment environments. Distributionally Robust Optimization (DRO) offers a promising framework by optimizing worst-case performance over a set of candidate distributions, which is called as the \emph{uncertainty set}. However, the efficacy of DRO heavily depends on the design of uncertainty set, and existing methods often perform suboptimally due to inappropriate and inflexible uncertainty sets. In this work, we first propose a novel perspective that casts entropy-regularized Wasserstein DRO as a dynamic process of distributional exploration and semantic alignment, both driven by optimal transport (OT). This unified viewpoint yields two key new techniques: \emph{semantic calibration}, which bootstraps semantically meaningful transport costs via inverse OT, and \emph{adaptive refinement}, which adjusts uncertainty set using OT-driven feedback. Together, these components form an exploration-and-feedback system, where the transport costs and uncertainty set evolve jointly during training, enabling the model to better adapt to potential distribution shifts. Moreover, we provide an in-depth analysis on this adaptive process and prove the theoretical convergence guarantee. Finally, we present our experimental results across diverse distribution shift scenarios, which demonstrate that our approach significantly outperforms existing methods, achieving state-of-the-art robustness.

The problem of contract design addresses the challenge of moral hazard in principle-agent setups. The agent exerts costly efforts that produce a random outcome with an associated reward for the principal. Moral hazard refers to the tension that the principal cannot observe the agent’s effort level hence needs to incentivize the agent only through rewarding the realized effort outcome, i.e., the contract. Bayesian contract design studies the principal’s design problem of an optimal contract when facing an unknown agent characterized by a private Bayesian type. In its most general form, the agent’s type is inherently “multi-parameter” and can arbitrarily affect both the agent’s productivity and effort costs. In contrast, a natural single-parameter setting of much recent interest simplifies the agent’s type to a single value that describes the agent’s cost per unit of effort, whereas agents’ efforts are assumed to be equally productive.

The stack loading problem has been studied in recent years for its great impact on the container loading and unloading operations. Among different objectives of the problem considered, minimizing the total number of unordered stackings and minimizing the total number of used stacks are the two important ones, which ensure efficient loading and unloading schedules, as well as reduce storage costs, respectively. The load-bearing setting, where each container has its own weight and bearing weight, is frequently considered in box packing operations but rarely in the existing studies on the stack loading problem. However, the load-bearing constraint on containers is very important for stack loading, because safety is of paramount importance. This paper is the first study on the stack loading problem with the load-bearing constraint with an aim to minimize the number of stacks and the number of unordered stackings. We show that this problem is strongly$\mathcal{NP}$-hard even when the number of stacks is given and equals$2$. For the case where the number of stacks is given and jobs on the bottom tiers are fixed, we show that the problem can be solved by dynamic programming in pseudo-polynomial time. For the general problem, based on a two-index integer linear programming formulation and a tabu search heuristic, we develop a binary-search based matheuristic. Our experimental results demonstrate the efficiency and effectiveness of the newly developed matheuristic.Note to Practitioners—This paper is motivated by the stack loading problem and is the first study on the load-bearing limit case. The load-bearing limit is a fundamental constraint but has not been taken into account in studies in the stack loading problem. Based on ISO Standard 1496, the corner posts and corner fittings of ISO Series I containers can bear a certain amount of weight. If the total weight of the containers above exceeds the load-bearing limit of the lower container, it will hazard the load-bearing safety. This paper proposes two problem formulations: three-index formulation and two-index formulation. The three-index formulation adds the load-bearing limit to the existing stack loading problem formulation. It turns out that the traditional three-index formulation of the stack loading problem is not efficient when being used in solving the problem with load-bearing constraints. Therefore, we propose a new two-index formulation. Apart from the theoretical results, this paper proposes a matheuristic solution framework: firstly, using binary search with greedy matheuristic for feasibility checking to minimize the number of stacks, and secondly, using tabu search matheuristic to minimize the number of unordered stackings. In future research, we will apply the matheuristic to different types of container scenarios and the parallel stack loading case.

Mobile crowdsourcing has emerged as a popular approach for organizations to leverage the collective intelligence of a crowd of users to obtain services. Considering users’ costs for providing services, it is vital for the requester to design incentive mechanisms to encourage users’ participation in crowdsourcing under the budget constraint. This aligns with the concept of budget-feasible mechanism design. Existing budget-feasible mechanisms often assume immediate user reachability and willingness of joining the crowdsourcing, which is unrealistic. To address this issue, a promising approach is to have participating users diffuse auction information to potential users in the social network. However, this brings another challenge in that participating users can be strategic and therefore hesitant to invite more potential competitors to join the crowdsourcing platform. In this paper, we focus on developing diffusion mechanisms that incentivize strategic users to actively diffuse auction information through the social network. This helps to attract more informed users and ultimately increases the value of the procured services. Specifically, we propose optimal budget-feasible diffusion mechanisms that simultaneously guarantee individual rationality, budget-feasibility, strong budget-balance, incentive-compatibility (i.e., users report real costs and diffuse auction information to all their neighbors) and approximation. Experiment results under real datasets further demonstrate the efficiency of proposed mechanisms.

We study the group-fair obnoxious facility location problems from the mechanism design perspective where agents belong to different groups and have private location preferences on the undesirable locations of the facility. Our main goal is to design strategyproof mechanisms that elicit the true location preferences from the agents and determine a facility location that approximately optimizes several group-fair objectives. We first consider the maximum total and average group cost (group-fair) objectives. For these objectives, we propose deterministic mechanisms that achieve 3-approximation ratios and provide matching lower bounds. We then provide the characterization of 2-candidate strategyproof randomized mechanisms. Leveraging the characterization, we design randomized mechanisms with improved approximation ratios of 2 for both objectives. We also provide randomized lower bounds of 5/4 for both objectives. Moreover, we investigate intergroup and intragroup fairness (IIF) objectives, addressing fairness between groups and within each group. We present a mechanism that achieves a 4-approximation for the IIF objectives and provide tight lower bounds.

We study the facility location problems (FLPs) with altruistic agents who act to benefit others in their affiliated groups. Our aim is to design mechanisms that elicit true locations from the agents in different overlapping groups and place a facility to serve agents to approximately optimize a given objective based on agents' costs to the facility. Existing studies of FLPs consider myopic agents who aim to minimize their own costs to the facility. We mainly consider altruistic agents with well-motivated group costs that are defined over costs incurred by all agents in their groups. Accordingly, we define Pareto strategyproofness to account for altruistic agents and their multiple group memberships with incomparable group costs. We consider mechanisms satisfying this strategyproofness under various combinations of the planner's objectives and agents' group costs. For each of these settings, we provide upper and lower bounds of approximation ratios of the mechanisms satisfying Pareto strategyproofness.

We initiate the study of fair allocation with the set of divisible or indivisible items distributed in multiple regions. The key requirement is that each agent can only obtain items from one region. In this work, we consider two kinds of fairness concepts: envy-based notions including envy-freeness (EF) and envy-freeness up to one/any item (EF1/EFX), and share-based notions including proportionality (PROP) and proportionality up to one/any item (PROP1/PROPX). On the negative side, we show NP-hardness and inapproximability results about the aforementioned fairness notions. On the positive side, we propose several algorithms to compute the partial allocations that satisfy envy-based notions and allocations that approximate the above fairness notions.

We study information design in click-through auctions, in which the bidders/advertisers bid for winning an opportunity to show their ads but only pay for realized clicks. The payment may or may not happen, and its probability is called the click-through rate (CTR). This auction format is widely used in the industry of online advertising. Bidders have private values, whereas the seller has private information about each bidder’s CTRs. We are interested in the seller’s problem of partially revealing CTR information to maximize revenue. Information design in click-through auctions turns out to be intriguingly different from almost all previous studies in this space since any revealed information about CTRs will never affect bidders’ bidding behaviors – they will always bid their true value per click – but only affect the auction’s allocation and payment rule. In some sense, this makes information design effectively a constrained mechanism design problem. Our first result is an FPTAS to compute an approximately optimal mechanism under a constant number of bidders. The design of this algorithm leverages Bayesian bidder values which help to “smooth” the seller’s revenue function and lead to better tractability. The design of this FPTAS is complex and primarily algorithmic. Our second main result pursues the design of “simple” mechanisms that are approximately optimal yet more practical. We primarily focus on the two-bidder situation, which is already notoriously challenging as demonstrated in recent works. When bidders’ CTR distribution is symmetric, we develop a simple prior-free signaling scheme, whose construction relies on a parameter termed optimal signal ratio. The constructed scheme provably obtains a good approximation as long as the maximum and minimum of bidders’ value density functions do not differ much. © Junjie Chen, Minming Li, Haifeng Xu, and Song Zuo.

We study various models for the one-dimensional multi-stage facility location problems with transient agents, where a transient agent arrives in some stage and stays for a number of consecutive stages. In the problems, we need to serve each agent in one of their stages by determining the location of the facility at each stage. In the first model, we assume there is no cost for moving the facility across the stages. We focus on optimal algorithms to minimize both the social cost objective, defined as the total distance of all agents to the facility over all stages, and the maximum cost objective, defined as the max distance of any agent to the facility over all stages. For each objective, we give a slice-wise polynomial (XP) algorithm (i.e., solvable in m^f(k) for some fixed parameter k and computable function f, where m is the input size) and show that there is a polynomial-time algorithm when a natural first-come-first-serve (FCFS) order of agent serving is enforced. We then consider the mechanism design problem, where the agents' locations and arrival stages are private, and design a group strategy-proof mechanism that achieves good approximation ratios for both objectives and settings with and without FCFS ordering. In the second model, we consider the facility's moving cost between adjacent stages under the social cost objective, which accounts for the total moving distance of the facility. Correspondingly, we design XP (and polynomial time) algorithms and a group strategy-proof mechanism for settings with or without the FCFS ordering.

Scheduling with testing falls under the umbrella of the research on optimization with explorable uncertainty. In this model, each job has an upper limit on its processing time that can be decreased to a lower limit (possibly unknown) by some preliminary action (testing). Recently, D{ü}rr et al. \cite{DBLP:journals/algorithmica/DurrEMM20} has studied a setting where testing a job takes a unit time, and the goal is to minimize total completion time or makespan on a single machine. In this paper, we extend their problem to the budget setting in which each test consumes a job-specific cost, and we require that the total testing cost cannot exceed a given budget. We consider the offline variant (the lower processing time is known) and the oblivious variant (the lower processing time is unknown) and aim to minimize the total completion time or makespan on a single machine. For the total completion time objective, we show NP-hardness and derive a PTAS for the offline variant based on a novel LP rounding scheme. We give a $(4+ε)$-competitive algorithm for the oblivious variant based on a framework inspired by the worst-case lower-bound instance. For the makespan objective, we give an FPTAS for the offline variant and a $(2+ε)$-competitive algorithm for the oblivious variant. Our algorithms for the oblivious variants under both objectives run in time $O(poly(n/ε))$. Lastly, we show that our results are essentially optimal by providing matching lower bounds.

The real-world deployment of fair allocation algorithms usually involves a heterogeneous population of users, which makes it challenging for the users to get complete knowledge of the allocation except for their own bundles. Recently, a new fairness notion, maximin-awareness (MMA) was proposed and it guarantees that every agent is not the worst-off one, no matter how the items that are not allocated to this agent are distributed. We adapt and generalize this notion to the case of indivisible chores and when the agents may have arbitrary weights. Due to the inherent difficulty of MMA, we also consider its up to one and up to any relaxations. A string of results on the existence and computation of MMA related fair allocations, and their connections to existing fairness concepts is given.

To meet increasing demands for machine-learning-based applications, pushing inference services to the network edge has been a trend. This work aims to design an on-demand edge inference scheduler with accuracy and deadline guarantee for repetitive tasks. Specifically, we consider an edge server that is preinstalled with multiple early-exit Deep Neural Networks (DNNs), and each DNN-exit pair can provide inference service of different quality. We also consider tasks' diversity in quality of service requirements and related utility. We aim to maximize the system's total utility by optimizing service assignment and time scheduling subject to resource, accuracy, and deadline constraints. We present this problem's integer linear problem formulation and show this problem is NP-hard even for the offline case. This problem is challenging due to the coupled effect of service assignment and time scheduling. To derive low-complexity scheduling solutions, we introduce a task-service graph and convert this problem into a service assignment selection problem with schedulability constraints. Then, we design a polynomial complexity algorithm with$\frac{\rho}{\delta}$-approximation ratio for the offline problem, with$\rho$referring to the task-wise utility ratio,$\delta$referring to the maximum number of concurrent tasks. To handle the online problem, we propose an online heuristic algorithm. Simulation results show that the proposed algorithms outperform the state-of-the-art baseline algorithms.

In the classic network security games, the defender distributes defending resources to the nodes of the network, and the attacker attacks a node, with the objective of maximizing the damage caused. In this paper, we consider the network defending problem against contagious attacks, e.g., the attack at a node u spreads to the neighbors of u and can cause damage at multiple nodes. Existing works that study shared resources assume that the resource allocated to a node can be shared or duplicated between neighboring nodes. However, in the real world, sharing resource naturally leads to a decrease in defending power of the source node, especially when defending against contagious attacks. Therefore, we study the model in which resources allocated to a node can only be transferred to its neighboring nodes, which we refer to as a reallocation process. We show that the problem of computing optimal defending strategy is NP-hard even for some very special cases. For positive results, we give a mixed integer linear program formulation for the problem and a bi-criteria approximation algorithm. Our experimental results demonstrate that the allocation and reallocation strategies our algorithm computes perform well in terms of minimizing the damage due to contagious attacks.

In a crowdsensing platform, users are invited to provide data services, and multiple requesters compete for desired services. Due to users' costs of providing services, it is critical to design incentive mechanisms to incentivize users with (monetary) rewards. Meanwhile, requesters may have individual budgets and compete for services with different procurement abilities. Such a setting falls into the budget-feasible mechanism design. However, most of the existing budget-feasible mechanisms focus on one-sided markets with a single requester rather than the two-sided markets with multiple requesters having different procurement abilities. Moreover, requesters and users can be selfish and strategic with their private information, which requires preventing information manipulation on both requesters' and users' sides. In this paper, we investigate budget-feasible mechanisms in two-sided crowdsensing markets where multiple strategic requesters come with private budgets to obtain services from the strategic users. We also consider the fairness on the requesters' side,i.e., a requester with more budget should obtain more service. We propose budget-feasible mechanisms for two models by distinguishing the types of services,i.e., the homogeneous or heterogeneous services. All proposed mechanisms satisfy fairness, budget feasibility, truthfulness on both users' and requesters' sides, and the constant approximation ratio. Numerical experiment results further demonstrate the efficiency of our proposed mechanisms.

We consider a new problem of selling data to a machine learner who looks to purchase data to train his machine learning model. A key challenge in this setup is that neither the seller nor the machine learner knows the true quality of data. When designing a revenue-maximizing mechanism, a data seller faces the tradeoff between the cost and precision of data quality estimation. To address this challenge, we study a natural class of mechanisms that price data via costly signaling. Motivated by the assumption of i.i.d. data points as in classic machine learning models, we first consider selling homogeneous data and derive an optimal selling mechanism. We then turn to the sale of heterogeneous data, motivated by the sale of multiple data sets, and show that 1) on the negative side, it is NP-hard to approximate the optimal mechanism within a constant ratio e/(e+1) + o(1); while 2) on the positive side, there is a 1/k-approximate algorithm, where k is the number of the machine learner’s private types.

The Stackelberg security game is played between a defender and an attacker, where the defender needs to allocate a limited amount of resources to multiple targets in order to minimize the loss due to adversarial attack by the attacker. While allowing targets to have different values, classic settings often assume uniform requirements to defend the targets. This enables existing results that study mixed strategies (randomized allocation algorithms) to adopt a compact representation of the mixed strategies. In this work, we initiate the study of mixed strategies for the security games in which the targets can have different defending requirements. In contrast to the case of uniform defending requirement, for which an optimal mixed strategy can be computed efficiently, we show that computing the optimal mixed strategy is NP-hard for the general defending requirements setting. However, we show that strong upper and lower bounds for the optimal mixed strategy defending result can be derived. We propose an efficient close-to-optimal Patching algorithm that computes mixed strategies that use only few pure strategies. We also study the setting when the game is played on a network and resource sharing is enabled between neighboring targets. Our experimental results demonstrate the effectiveness of our algorithm in several large real-world datasets.

We study the facility location problems where agents are located on a real line and divided into groups based on criteria such as ethnicity or age. Our aim is to design mechanisms to locate a facility to approximately minimize the costs of groups of agents to the facility fairly while eliciting the agents' locations truthfully. We first explore various well-motivated group fairness cost objectives for the problems and show that many natural objectives have an unbounded approximation ratio. We then consider minimizing the maximum total group cost and minimizing the average group cost objectives. For these objectives, we show that existing classical mechanisms (e.g., median) and new group-based mechanisms provide bounded approximation ratios, where the group-based mechanisms can achieve better ratios. We also provide lower bounds for both objectives. To measure fairness between groups and within each group, we study a new notion of intergroup and intragroup fairness (IIF) . We consider two IIF objectives and provide mechanisms with tight approximation ratios.

Nowadays cloud providers purchase a good deal of bandwidth from Internet service providers to satisfy the growing requests from corporate customers for the exclusive use of inter-datacenter bandwidth. For exclusive bandwidth services, neither maximizing the revenue nor minimizing the cost can bring the maximal profit to cloud providers. The diversity of bandwidth prices and the random arrival time of user requests further increase the difficulty in economically scheduling the services to meet user requests from cloud providers. In this article, we propose to help cloud providers maximize their service profits by properly selecting user requests to serve rather than satisfying them all. We formulate the problem of service profit maximization and prove its NP-hardness. To handle offline request submission, we propose a solution that maximizes the service profit by alternately maximizing the service revenue and minimizing the service cost. To maximize service profit under online request submission, we propose an online scheduling algorithm that carefully handles the risk of not being able to pay off the incremental service cost and makes scheduling decisions in real time. Our extensive evaluations demonstrate that our solutions can achieve more than 1.6x the service profits of existing solutions.

We study the problem faced by a decision maker who wants to locate a set of facilities on a real line and allocate agents/items to the facilities. The items have given locations on the line, and can only be assigned to one of their closest facilities. The facilities are controlled by managers, who have additive utility over the items. An optimal solution that maximizes the (utilitarian or egalitarian) social welfare of the facilities may present a very unbalanced allocation of the items to the facilities and hence be perceived as unfair. In this paper, we are interested in fair allocation among facility managers and consider the well-studied proportionality and envy-freeness fairness notions and their relaxations. We assess the availability, existence, approximability, and the quality (price of fairness) of fair solutions, where the quality measures the system efficiency loss under a fair allocation compared to the one that maximizes the social welfare. Further, we show that one can find a Pareto-optimal solution in polynomial time.

In classic network security games, the defender distributes defending resources to the nodes of the network, and the attacker attacks a node, with the objective to maximize the damage caused. Existing models assume that the attack at node u causes damage only at u. However, in many real-world security scenarios, the attack at a node u spreads to the neighbors of u and can cause damage at multiple nodes, e.g., for the outbreak of a virus. In this paper, we consider the network defending problem against contagious attacks. Existing works that study shared resources assume that the resource allocated to a node can be shared or duplicated between neighboring nodes. However, in real world, sharing resource naturally leads to a decrease in defending power of the source node, especially when defending against contagious attacks. To this end, we study the model in which resources allocated to a node can only be transferred to its neighboring nodes, which we refer to as a reallocation process. We show that this more general model is difficult in two aspects: (1) even for a fixed allocation of resources, we show that computing the optimal reallocation is NP-hard; (2) for the case when reallocation is not allowed, we show that computing the optimal allocation (against contagious attack) is also NP-hard. For positive results, we give a mixed integer linear program formulation for the problem and a bi-criteria approximation algorithm. Our experimental results demonstrate that the allocation and reallocation strategies our algorithm computes perform well in terms of minimizing the damage due to contagious attacks.

This paper studies the budget-feasible mechanism design over graphs, where a buyer wishes to procure items from sellers, and all participants (the buyer and sellers) can only directly interact with their neighbors during the auction campaign. The problem for the buyer is to use the limited budget to incentivize sellers to propagate auction information to their neighbors, thereby more sellers will be informed of the auction and more item value will be procured. An impossibility result shows that the large-market assumption is necessary. We propose efficient budget-feasible diffusion mechanisms for large markets that simultaneously guarantee individual rationality, budget-feasibility, strong budget-balance, incentive-compatibility to report private costs and diffuse auction information. Moreover, the proposed mechanisms achieve logarithmic approximation that the total procured value is within a logarithmic factor of the optimal solution. Compared to most related budget-feasible mechanisms, which do not take the individual interactions among sellers into account, our mechanisms can incentivize sellers to further propagate auction information to other potential sellers. Meanwhile, existing related diffusion mechanisms only focus on seller-centric auctions and fail to satisfy the budget-feasibility of the buyer.

The study of approximate mechanism design for facility location has been in the center of research at the intersection of artificial intelligence and economics for the last decade, largely due to its practical importance in various domains, such as social planning and clustering. At a high level, the goal is to select a number of locations on which to build a set of facilities, aiming to optimize some social objective based on the preferences of strategic agents, who might have incentives to misreport their private information. This paper presents a comprehensive survey of the significant progress that has been made since the introduction of the problem, highlighting all the different variants and methodologies, as well as the most interesting directions for future research.

In this paper, we consider the problem of designing budget-feasible mechanisms for selecting agents with private costs from various groups to ensure proportional representation, where the minimum proportion of the selected agents from each group is maximized. Depending on agents' membership in the groups, we consider two main models: single group setting where each agent belongs to only one group, and multiple group setting where each agent may belong to multiple groups. We propose novel budget-feasible proportion-representative mechanisms for these models, which can select representative agents from different groups. The proposed mechanisms guarantee theoretical properties of individual rationality, budget-feasibility, truthfulness, and approximation performance on proportional representation.

We study a fair resource scheduling problem, where a set of interval jobs are to be allocated to heterogeneous machines controlled by intellectual agents.Each job is associated with release time, deadline, and processing time such that it can be processed if its complete processing period is between its release time and deadline. The machines gain possibly different utilities by processing different jobs, and all jobs assigned to the same machine should be processed without overlap.We consider two widely studied solution concepts, namely, maximin share fairness and envy-freeness.For both criteria, we discuss the extent to which fair allocations exist and present constant approximation algorithms for various settings.

Real-time end-to-end task scheduling in networked control systems (NCSs) requires the joint consideration of both network and computing resources to guarantee the desired quality of service (QoS). This paper introduces a new model for composite resource scheduling (CRS) in real-time networked control systems, which considers a strict execution order of sensing, computing, and actuating segments based on the control loop of the target NCS. We prove that the general CRS problem is NP-hard and study two special cases of the CRS problem. The first case restricts the computing and actuating segments to have unit-size execution time while the second case assumes that both sensing and actuating segments have unit-size execution time. We propose an optimal algorithm to solve the first case by checking the intervals with 100% network resource utilization and modify the deadlines of the tasks within those intervals to prune the search. For the second case, we propose another optimal algorithm based on a novel backtracking strategy to check the time intervals with the network resource utilization larger than 100% and modify the timing parameters of tasks based on these intervals. For the general case, we design a greedy strategy to modify the timing parameters of both network segments and computing segments within the time intervals that have network and computing resource utilization larger than 100%, respectively. The correctness and effectiveness of the proposed algorithms are verified through extensive experiments.

We introduce the problem of maximizing approximately $k$-submodular functions subject to size constraints. In this problem, one seeks to select $k$-disjoint subsets of a ground set with bounded total size or individual sizes, and maximum utility, given by a function that is "close" to being $k$-submodular. The problem finds applications in tasks such as sensor placement, where one wishes to install $k$ types of sensors whose measurements are noisy, and influence maximization, where one seeks to advertise $k$ topics to users of a social network whose level of influence is uncertain. To deal with the problem, we first provide two natural definitions for approximately $k$-submodular functions and establish a hierarchical relationship between them. Next, we show that simple greedy algorithms offer approximation guarantees for different types of size constraints. Last, we demonstrate experimentally that the greedy algorithms are effective in sensor placement and influence maximization problems.

We study the mechanism design problem of a social planner for locating two facilities on a line interval [0, 1], where a set of n strategic agents report their locations and a mechanism determines the locations of the two facilities. We consider the requirement of a minimum distance 0 ≤ d ≤ 1 between the two facilities. Given the two facilities are heterogeneous, we model the cost/utility of an agent as the sum of his distances to both facilities. In the heterogeneous two-facility location game to minimize the social cost, we show that the optimal solution can be computed in polynomial time and prove that carefully choosing one optimal solution as output is strategyproof. We also design a strategyproof mechanism minimizing the maximum cost. Given the two facilities are homogeneous, we model the cost/utility of an agent as his distance to the closer facility. In the homogeneous two-facility location game for minimizing the social cost, we show that any deterministic strategyproof mechanism has unbounded approximation ratio. Moreover, in the obnoxious heterogeneous two-facility location game for maximizing the social utility, we propose new deterministic group strategyproof mechanisms with provable approximation ratios and establish a lower bound (7 − d)/6 for any deterministic strategyproof mechanism. We also design a strategyproof mechanism maximizing the minimum utility. In the obnoxious homogeneous two-facility location game for maximizing the social utility, we propose deterministic group strategyproof mechanisms with provable approximation ratios and establish a lower bound 4/3. Besides, in the two-facility location game with triple-preference, where each facility may be favorable, obnoxious, indifferent for any agent, we further motivate agents to report both their locations and preferences towards the two facilities truthfully, and design a deterministic group strategyproof mechanism with an approximation ratio 4.

Unmanned Aerial Vehicle (UAV) have emerged as a promising technique to rapidly provide wireless services to a group of mobile users simultaneously. The article aims to address a challenging issue that each user is selfish and may misreport his location or preference for changing the optimal UAV location to be close to himself. Using algorithmic game theory, we study how to determine the final location of a UAV in the 3D space, by ensuring all selfish users' truthfulness in reporting their locations for learning purpose. To minimize the social service cost in this UAV placement game, we design strategyproof mechanisms with the approximation ratios, when comparing to the social optimum. We also study the obnoxious UAV placement game to maximally keep their social utility, where each incumbent user may misreport his location to keep the UAV away from him. Moreover, we present the dual-preference UAV placement game by considering the coexistence of the two groups of users above, where users can misreport both their locations and preference types (favorable or obnoxious) towards the UAV. Finally, we extend the three games above to include multiple UAVs and design strategyproof mechanisms with provable approximation ratios.

We study single-candidate voting embedded in a metric space, where both voters and candidates are points in the space, and the distances between voters and candidates specify the voters' preferences over candidates. In the voting, each voter is asked to submit her favorite candidate. Given the collection of favorite candidates, a mechanism for eliminating the least popular candidate finds a committee containing all candidates but the one to be eliminated. Each committee is associated with a social value that is the sum of the costs (utilities) it imposes (provides) to the voters. We design mechanisms for finding a committee to optimize the social value. We measure the quality of a mechanism by its distortion, defined as the worst-case ratio between the social value of the committee found by the mechanism and the optimal one. We establish new upper and lower bounds on the distortion of mechanisms in this single-candidate voting, for both general metrics and well-motivated special cases.

In this paper we consider a defending problem on a network. In the model, the defender holds a total defending resource of R, which can be distributed to the nodes of the network. The defending resource allocated to a node can be shared by its neighbors. There is a weight associated with every edge that represents the efficiency defending resources are shared between neighboring nodes. We consider the setting when each attack can affect not only the target node, but its neighbors as well. Assuming that nodes in the network have different treasures to defend and different defending requirements, the defender aims at allocating the defending resource to the nodes to minimize the loss due to attack. We give polynomial time exact algorithms for two important special cases of the network defending problem. For the case when an attack can only affect the target node, we present an LP-based exact algorithm. For the case when defending resources cannot be shared, we present a max-flow-based exact algorithm. We show that the general problem is NP-hard, and we give a 2-approximation algorithm based on LP-rounding. Moreover, by giving a matching lower bound of 2 on the integrality gap on the LP relaxation, we show that our rounding is tight.

This paper studies the facility location games with payments, where facilities are strategic players. In the game, customers and facilities are located at publicly known locations on a line segment. Each selfish facility has an opening-cost as her private information, and she may strategically report it. Upon receiving the reports, the government uses a mechanism to select some facilities to open and pay to them. The cost/utility of each customer depends on the distance to the nearest opened facility. Under a given budget B, which constrains the total payment, we derive upper and lower bounds on the approximation ratios of truthful budget feasible mechanisms for four utilitarian and egalitarian objectives, and study the case when augmented budget is allowed.

In this paper, we study the two-facility location game with optional preference where the acceptable set of facilities for each agent could be different and an agent's cost is his distance to the closest facility within his acceptable set. The objective is to minimize the total cost of all agents while achieving strategyproofness. For general metrics, we design a deterministic strategyproof mechanism for the problem with approximation ratio of 1+2alpha, where alpha is the approximation ratio of the optimization version. In particular, for the setting on a line, we improve the earlier best ratio of n/2+1 to a ratio of 2.75.

With the proliferation of globally-distributed services and the quick growth of user requests for inter-datacenter bandwidth, cloud providers have to lease a good deal of bandwidth from Internet service providers to satisfy the user demands. Neither maximizing the service revenue nor minimizing the service cost can bring the maximal service profit to cloud providers. The diversity of user requests and the large unit of inter-datacenter bandwidth further increase the difficulty of scheduling user requests. In this paper, we propose a cloud operational model to help cloud providers to make more service profit by properly selecting requests to serve rather than serving all user requests. We formulate the problem of service profit maximization and prove its NP-hardness. Considering the complicated coupling between maximizing revenue and minimizing cost, we propose a framework, Metis, for the efficient scheduling of user requests over inter-datacenter networks to maximize the service profit for cloud providers. Metis is formed with the alternate operations of two algorithms derived from randomized rounding techniques and Chernoff-Hoeffding bound. We prove that they can provide the guarantees on approximation ratios. Our extensive evaluations demonstrate that Metis can achieve more than 1.3x the service profits of existing solutions.

Many previous studies attempt to utilize information from other domains to achieve better performance of recommendation. Recently, social information has been shown effective in improving recommendation results with transfer learning frameworks, and the transfer part helps to learn users' preferences from both item domain and social domain. However, two vital issues have not been well-considered in existing methods: 1) Usually, a static transfer scheme is adopted to share a user's common preference between item and social domains, which is not robust in real life where the degrees of sharing and information richness are varied for different users. Hence a non-personalized transfer scheme may be insufficient and unsuccessful. 2) Most previous neural recommendation methods rely on negative sampling in training to increase computational efficiency, which makes them highly sensitive to sampling strategies and hence difficult to achieve optimal results in practical applications.

We study the scheduling problem with calibrations. In 2013, Bender et al. (SPAA '13) proposed a theoretical framework for the problem. Jobs of unit processing time with release times and deadlines are to be scheduled on parallel identical machines. The machines need to be calibrated to run jobs while a single calibration remains valid on a machine only for a time period of length T. The objective is to find a schedule that completes all jobs within their timing constraints and minimizes the total number of calibrations. In this paper, we aim to design an approximation algorithm to solve the problem. We propose a dynamic programming algorithm with polynomial running time when the number of machines is constant. In addition, we give a PTAS when the number of machines is input.

The problem of pollution control has been mainly studied in the environmental economics literature where the methodology of game theory is applied for the pollution control. To the best of our knowledge this is the first time this problem is studied from the computational point of view. We introduce a new network model for pollution control and present two applications of this model. On a high level, our model comprises a graph whose nodes represent the agents, which can be thought of as the sources of pollution in the network. The edges between agents represent the effect of spread of pollution. The government who is the regulator, is responsible for the maximization of the social welfare and sets bounds on the levels of emitted pollution in both local areas as well as globally in the whole network. We first prove that the above optimization problem is NP-hard even on some special cases of graphs such as trees. We then turn our attention on the classes of trees and planar graphs which model realistic scenarios of the emitted pollution in water and air, respectively. We derive approximation algorithms for these two kinds of networks and provide deterministic truthful and truthful in expectation mechanisms. In some settings of the problem that we study, we achieve the best possible approximation results under standard complexity theoretic assumptions. Our approximation algorithm on planar graphs is obtained by a novel decomposition technique to deal with constraints on vertices. We note that no known planar decomposition techniques can be used here and our technique can be of independent interest. For trees we design a two level dynamic programming approach to obtain an FPTAS. This approach is crucial to deal with the global pollution quota constraint. It uses a special multiple choice, multi-dimensional knapsack problem where coefficients of all constraints except one are bounded by a polynomial of the input size. We furthermore derive truthful in expectation mechanisms on general networks with bounded degree.

Maintaining the temporal validity of real-time data in cyber-physical systems is of critical importance to ensure the correct decision making and appropriate system operation. Most existing work on real-time data retrieval assume that the real-time data under study are always available for retrieval, and the developed scheduling algorithms mainly focus on making real-time decisions while meeting the temporal validity constraints. This assumption, however does not hold in many real-time applications with intermittent data availability. In this paper, we study the Availability-constrained Fresh Data Retrieval (AFDR) problem, which aims to retrieve all required real-time data for a given set of decision tasks on time while taking both the temporal validity and data availability constraints into consideration. We formulate the AFDR problem as an ILP problem and study its complexity under different settings. Given the general case of the AFDR problem is proved to be NP-hard, we focus on the cases that data items have unit-size retrieval time. For the single decision task scenario, we propose a polynomial-time optimal data retrieval algorithm, which consists of a task finish time selection phase and an optimal retrieval schedule construction phase, to solve the AFDR problem. For the multiple decision task scenario, we propose an efficient heuristic algorithm by transforming the temporal validity constraint of a real-time data item to the availability constraint. The effectiveness of the proposed algorithms has been validated through extensive experiments. Our results show that the heuristic algorithm outputs around $1.5\times$1.5× feasible cases compared to that of the state-of-the-art scheme.

Cloud computing platforms enable applications to offer low-latency services to users by deploying data storage in multiple geo-distributed data centers. In this paper, through benchmark measurements on Amazon AWS and Microsoft Azure together with an analysis of a large-scale dataset collected from a major cloud CDN provider, we identify the high tail latency problem in cloud CDNs, which can substantially undermine the efficacy of cloud CDNs. One crucial idea to reduce the tail latency is to send requests in parallel to multiple clouds in cloud CDNs. However, since application providers often have a budget for using cloud services, deciding how many chunks to download from each cloud and when to download chunks in a cost-efficient manner still remain as open problems in our concerned scenario. To address the problem, we present TailCutter, a workload scheduling framework that aims at optimizing the tail latency while meeting cost constraints given by application providers. Specifically, we formulate the tail latency minimization (TLM) problem in cloud CDNs and design the receding horizon control based maximum tail minimization algorithm (RHC-based MTMA) to efficiently solve the TLM problem in practice. We implement TailCutter across multiple data centers of Amazon AWS and Microsoft Azure. Extensive evaluations using a large-scale real-world data trace (collected from a major ISP) illustrate that TailCutter can reduce up to 58.9% of the 100th-percentile user-perceived latency, as compared with alternative solutions under the cost constraint.

With the quick growth of traffic between data centers, inefficient transfer scheduling in inter-datacenter networks can lead to a huge waste of bandwidth thus significant bandwidth cost. Previous work have explored different ways, such as software-defined WANs and dynamic pricing mechanisms, to overcome the inefficiency of inter-datacenter networks. However, there is a big challenge in addressing the fundamental conflicts between the deadline-aware transfer scheduling and minimizing the bandwidth cost. Unlike existing efforts that schedule inter-datacenter transfers under fixed link capacities, wherein some deadlines are violated and the service quality is degraded, we aim to finish all the transfers on time with as little bandwidth as possible to minimize the bandwidth cost. We take into account the variation of bandwidth price and the deadline requirements of services, and formulate the problem of cost-efficient scheduling of bulk transfers with deadline guarantee, which is shown to be NP-hard. Benefitting from the relax-and-round method, we propose a progressively-descending algorithm (PDA) to schedule bulk transfers and meet the above goals with a guaranteed approximation ratio. We apply our algorithm in a bulk transfer scheduler, Butler, and build a small-scale testbed to evaluate its efficiency. Both large-scale simulation and testbed experiment results validate the ability of our scheme on cutting down the bandwidth cost. Compared with existing approaches, it reduces up to 60% bandwidth cost and increases the network utilization by up to 140%.

In this paper, we propose a fractional preference model for the facility location game with two facilities that serve the similar purpose on a line where each agent has his location information as well as fractional preference to indicate how well they prefer the facilities. The preference for each facility is in the range of [0, L] such that the sum of the preference for all facilities is equal to 1. The utility is measured by subtracting the sum of the cost of both facilities from the total length L where the cost of facilities is defined as the multiplication of the fractional preference and the distance between the agent and the facilities. We first show that the lower bound for the objective of minimizing total cost is at least Ω(n^1/3). Hence, we use the utility function to analyze the agents' satification. Our objective is to place two facilities on [0, L] to maximize the social utility or the minimum utility. For each objective function, we propose deterministic strategy-proof mechanisms. For the objective of maximizing the social utility, we present an optimal deterministic strategy-proof mechanism in the case where agents can only misreport their locations. In the case where agents can only misreport their preferences, we present a 2-approximation deterministic strategy-proof mechanism. Finally, we present a 4-approximation deterministic strategy-proof mechanism and a randomized strategy-proof mechanism with an approximation ratio of 2 where agents can misreport both the preference and location information. Moreover, we also give a lower-bound of 1.06. For the objective of maximizing the minimum utility, we give a lower-bound of 1.5 and present a 2-approximation deterministic strategy-proof mechanism where agents can misreport both the preference and location.

This paper considers the mechanism design problem in two-sided markets where multiple strategic buyers come with budgets to procure as much value of items as possible from the strategic sellers. Each seller holds an item with public value and is allowed to bid its private cost. Buyers could claim their budgets, not necessarily the true ones. The goal is to seek budget-feasible mechanisms that ensure sellers are rewarded enough payment and buyers' budgets are not exceeded. Our main contribution is a random mechanism that guarantees various desired theoretical guarantees like the budget feasibility, the truthfulness on the sellers' side and the buyers' side simultaneously, and constant approximation to the optimal total procured value of buyers.

Real-time task scheduling for wireless networked control systems provides guarantees for the quality of service. This paper introduces a new model for joint network and computing resource scheduling (JNCRS) in real-time wireless networked control systems. This new end-to-end real-time task model considers a strict execution order of segments including the sensing, the computing and the actuating segment based on the control loop of WNCSs. The general JNCRS problem is proved to be a NP-hard problem. After dividing the JNCRS problem into four subproblems, we propose a polynomial-time optimal algorithm to solve the first subproblem where each segment has unit execution time, by checking the intervals with 100% network resource utilization and modify the deadlines of tasks. To solve the second subproblem where the computing segment is larger than one unit execution time, we define the new timing parameters of each network segment by taking into account the scheduling of the computing segments. We propose a polynomial-time optimal algorithm to check the intervals with the network resource utilization larger than or equal to 100% and modify the timing parameters of tasks based on these intervals.

The following topics are dealt with: telecommunication scheduling; optimisation; cellular radio; wireless channels; probability; radio networks; mobile radio; cache storage; telecommunication traffic; and stochastic processes.

Cooperative cache has become a promising technique to optimize the traffic by caching big data in networks. However, controlling distributed cache nodes to update cached contents synergistically is still challenging in designing cooperative cache systems. This paper proposes an SDN-based Cooperative Cache Network (SCCN) for ISP networks, aiming to minimize the content transmission latency while reducing the inter-ISP traffic. Based on the proposed increment recording mechanism, the SCCN Controller can timely capture the change of content popularity, and place the most popular contents on the appropriate SCCN Switches. We formulate the optimal content placement as a specific multi-commodity facility location problem and prove its NP-hardness. We propose a Relaxation Algorithm (RA) based on relaxation-rounding technique to solve the problem, which can achieve an approximation ratio of 1/2 in the worst case. To solve large scale problems for big data efficiently, we further design a Heuristic Algorithm (HA), which can find a near-optimal solution with three orders of magnitude speedup compared to RA. Specifically, HA can achieve a desirable tradeoff between the transmission delay and the Internet traffic. We implement a prototype based on Open vSwitch to demonstrate the feasibility of SCCN. Extensive trace-based simulation results show the effectiveness of SCCN under various network conditions.

The rapid development of the Real-Time and Embedded System (RTES) has increased the requirement on the processing capabilities of sensors, mobiles and smart devices, etc. Meanwhile, energy efficiency techniques are in desperate need as most devices in RTES are battery powered. Following the above trends, this work explores the memory system energy efficiency for a general multi-core architecture. This architecture integrates a local memory in each processing core, with a large off-chip memory shared among multiple cores. Decisions need to be made on whether tasks will be executed with the shared memory or the local memory to minimize the total energy consumption within real-time constraints. This paper proposes optimal schemes as well as a polynomial-time approximation algorithm with constant ratio. The problem complexity analysis for different task and system models is also presented. Experimental results show that the proposed approximation scheme performs close to the optimal solution in average.

Maintaining the temporal validity of real-time data in cyber-physical systems (CPSs) is of critical importance to ensure correct decision making and appropriate system operation. Most existing work on real-time data retrieval assumes that the real-time data under study are always available, and the developed scheduling algorithms mainly focus on making real-time decisions while meeting the temporal validity (freshness) constraints. This assumption, however does not hold in many real-life CPS applications with intermittent data availability, such as in energy harvesting-based sensing systems. In this paper, we study the multi-interval availability-constrained fresh data retrieval (MAFDR) problem, which aims to retrieve all required real-time data on time for a set of decision tasks while taking both the temporal validity and data availability constraints into consideration. We present the formulation of the MAFDR problem and study its complexity under different settings. For the scenario of single decision task with unit-size data retrieval time, we propose a polynomial-time optimal data retrieval algorithm, which comprises a task finish time selection phase and an optimal retrieval schedule construction phase. For the general scenario of multiple decision tasks with nonunit-size data retrieval time, we provide an integer linear programming formulation for the MAFDR problem and propose a fast heuristic algorithm based on max flow. The effectiveness of the proposed algorithms has been validated through extensive experiments by comparing to the optimal solution and the state-of-the-art approach.

In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with pseudo-polynomial running time, and a fully polynomial-time approximation scheme (FPTAS).

In sensitive applications, machines need to be periodically calibrated to ensure that they run to high standards. Creating an efficient schedule on these machines requires attention to two metrics: ensuring good throughput of the jobs, and ensuring that not too much cost is spent on machine calibration. In this paper we examine flow time as a metric for scheduling with calibrations. While previous papers guaranteed that jobs would meet a certain deadline, we relax that constraint to a tradeoff: we want to balance how long the average job waits with how many costly calibrations we need to perform.

We study the problem of locating a single facility on a real line based on the reports of self-interested agents, when agents have double-peaked preferences, with the peaks being on opposite sides of their locations. We observe that double-peaked preferences capture real-life scenarios and thus complement the well-studied notion of single-peaked preferences. As a motivating example, assume that the government plans to build a primary school along a street; an agent with single-peaked preferences would prefer having the school built exactly next to her house. However, while that would make it very easy for her children to go to school, it would also introduce several problems, such as noise or parking congestion in the morning. A 5-min walking distance would be sufficiently far for such problems to no longer be much of a factor and at the same time sufficiently close for the school to be easily accessible by the children on foot. There are two positions (symmetrically) in each direction and those would be the agent’s two peaks of her double-peaked preference. Motivated by natural scenarios like the one described above, we mainly focus on the case where peaks are equidistant from the agents’ locations and discuss how our results extend to more general settings. We show that most of the results for single-peaked preferences do not directly apply to this setting, which makes the problem more challenging. As our main contribution, we present a simple truthful-in-expectation mechanism that achieves an approximation ratio of $$1+b/c$$ for both the social and the maximum cost, where b is the distance of the agent from the peak and c is the minimum cost of an agent. For the latter case, we provide a 3 / 2 lower bound on the approximation ratio of any truthful-in-expectation mechanism. We also study deterministic mechanisms under some natural conditions, proving lower bounds and approximation guarantees. We prove that among a large class of reasonable strategyproof mechanisms, there is no deterministic mechanism that outperforms our truthful-in-expectation mechanism. In order to obtain this result, we first characterize mechanisms for two agents that satisfy two simple properties; we use the same characterization to prove that no mechanism in this class can be group-strategyproof.

In crowdsourcing markets, a requester announces a task and calls for contribution from potential participants. With strategic participants, the requester needs to reward the participants to introduce the incentives of participation. However, it is natural to ask whether it is worth introducing incentives if the total payment for eliciting incentives is too high. This paper addresses such a fundamental concern by designing a frugal mechanism with minimum payment used to procure the total amount of service contributions demanded. We design two mechanisms to provide the incentives of participation while minimizing the payment used by the requester. We first propose a frugal auction-based mechanism, which stimulates participants to truthfully report their information. We theoretically prove that the payment used is not more than the optimal cost (with no incentive considered) plus a bounded additive. We then design a Stackelberg-game-based mechanism, in which the requester fixes a certain total payment at the very beginning so as to encourage the participants to compete for it and participate in the task. We verify the existence of a unique Nash equilibrium (NE) and develop a novel algorithm to find the NE, as well as the optimal payment to extract the NE. Our simulation results show that the payment used in these mechanisms is close to the optimal solution with no incentive considered, while the extra payment caused by introducing truthfulness in auction-based mechanism is about twice that of the NE in Stakelberg-game-based mechanism.

Non-Uniform Cache Architecture (NUCA) is a viable solution to mitigate the problem of large on-chip wire delay due to the rapid increase in the cache capacity of chip multiprocessors (CMPs). Through partitioning the last-level cache (LLC) into smaller banks connected by on-chip network, the access latency will exhibit non-uniform distribution. Various works have well explored the NUCA design, including block migration, block replication and block searching. However, all of the previous mechanisms designed for NUCA are thread-oblivious when multi-threaded applications are deployed on CMP systems. Due to the interference on shared resources, threads often demonstrate unbalanced progress wherein the lagging threads with slow progress are more critical to overall performance. In this paper, we propose a novel NUCA design called thread Criticality Assisted Replication and Migration (CARM). CARM exploits the runtime thread criticality information as hints to adjust the block replication and migration in NUCA. Specifically, CARM aims at boosting parallel application execution through prioritizing block replication and migration for critical threads. Full-system experimental results show that CARM reduces the execution time of a set of PARSEC workloads by 13.7 and 6.8 percent on average compared with the tradition D-NUCA and Re-NUCA respectively. Moreover, CARM also consumes much less energy compared with the evaluated schemes.

Chip manufacturers provide the Thermal Design Power (TDP) for a specific chip. The cooling solution is designed to dissipate this power level. But because TDP is not necessarily the maximum power that can be applied, chips are operated with Dynamic Thermal Management (DTM) techniques. To avoid excessive triggers of DTM, usually, system designers also use TDP as power constraint. However, using a single and constant value as power constraint, e.g., TDP, can result in significant performance losses in homogeneous and heterogeneous manycore systems. Having better power budgeting techniques is a major step towards dealing with the dark silicon problem. This paper presents a new power budget concept, called Thermal Safe Power (TSP), which is an abstraction that provides safe power and power density constraints as a function of the number of simultaneously active cores. Executing cores at any power consumption below TSP ensures that DTM is not triggered. TSP can be computed offline for the worst cases, or online for a particular mapping of cores. TSP can also serve as a fundamental tool for guiding task partitioning and core mapping decisions, specially when core heterogeneity or timing guarantees are involved. Moreover, TSP results in dark silicon estimations which are less pessimistic than estimations using constant power budgets.

Barrier coverage with wireless sensors aims at detecting intruders who attempt to cross a specific area, where wireless sensors are distributed remotely at random. This paper considers limited-power sensors with adjustable ranges deployed along a linear domain to form a barrier to detect intruding incidents. We introduce three objectives to minimize: 1) total power consumption while satisfying full coverage; 2) the number of active sensors to improve the reliability; and 3) the active sensor nodes' maximum sensing range to maintain fairness. We refer to the problem as the tradeoff barrier coverage (TBC) problem. With the aim of obtaining a better tradeoff among the three objectives, we present a multiobjective optimization framework based on multiobjective evolutionary algorithm (MOEA)/D, which is called problem specific MOEA/D (PS-MOEA/D). Specifically, we define a 2-tuple encoding scheme and introduce a cover-shrink algorithm to produce feasible and relatively optimal solutions. Subsequently, we incorporate problem-specific knowledge into local search, which allows search procedures for neighboring subproblems collaborate each other. By considering the problem characteristics, we analyze the complexity and incorporate a strategy of computational resource allocation into our algorithm. We validate our approach by comparing with four competitors through several most-used metrics. The experimental results demonstrate that PS-MOEA/D is effective and outperforms the four competitors in all the cases, which indicates that our approach is promising in dealing with TBC.

In cellular networks, it is important to conserve energy while at the same time satisfying different user performance requirements. In this paper, we first propose a comprehensive metric to capture the user performance cost due to task delay, deadline violation, different application profiles, and user preferences. We prove that finding the energy-optimal scheduling solution while meeting the requirements on the performance cost is NP-hard. Then, we design an adaptive online scheduling algorithm PerES to minimize the total energy cost on data transmissions subject to user performance constraints. We prove that PerES can make the energy consumption arbitrarily close to that of the optimal scheduling solution. Further, we develop offline algorithms to serve as the evaluation benchmark for PerES. The evaluation results demonstrate that PerES achieves average 2.5 times faster convergence speed compared to state-of-art static methods, and also higher performance than peers under various test conditions. Using 821 million traffic flows collected from a commercial cellular carrier, we verify our scheme could achieve on average 32-56 percent energy savings over the total transmission energy with different levels of user experience.

Device to Device communication enables the deployment of mobile cloudlets in LTE-advanced networks. The distributed nature of mobile users and dynamic task arrivals makes it challenging to schedule tasks fairly among multiple devices. Leveraging the idea of software defined networking, we propose a software defined cooperative offloading model (SDCOM), where the SDCOM controller is deployed at the PDN gateway and schedules tasks in a centralized manner to save the energy of mobile devices and reduce the traffic on access links. We formulate the minimum-energy task scheduling problem as a 0-1 knapsack problem and prove its NP-hardness. To compute the optimal solution as a benchmark, we design the conditioned optimal algorithm based on the aggregated analysis of energy consumption. The greedy algorithm with a polynominal-time complexity is proposed to solve large-scale problems efficiently. To address the problem without predicting future information on task arrivals, we further design an online task scheduling algorithm (OTS). It can minimize the energy consumption arbitrarily close to the optimal solution by appropriately setting the tradeoff coefficient. Moreover, we extend OTS to design a proportional fair online task scheduling algorithm to achieve the fair energy consumption among mobile devices. Extensive trace-based simulations demonstrate the effectiveness of SDCOM for a variety of typical mobile devices and applications.

Nowadays, memory energy reduction attracts significant attention as main memory consumes large amount of energy among all the energy consuming components. This paper focuses on reducing the energy consumption of the shared main memory in multicore processors by putting the memory into sleep state when all cores are idle. Based on this idea, we present systematic analysis of different models and propose a series of scheduling schemes to maximize the common idle time of all cores. The target problem is classified into two cases based on whether task migration is allowed or not among cores. Considering task migration, an optimal scheduling scheme is proposed, assuming the number of cores is unbounded. When the number of cores is bounded, an integer linear programming formulation and two efficient heuristic algorithms are proposed. When task migration is not allowed, we first prove the NP-hardness of the problem, and then propose the optimal solutions when task partitions are given in advance. The energy overhead caused by transitions between active and sleep modes of the memory is analyzed. The experimental results show that the heuristic algorithms work efficiently and can save 7.25% and 11.71% system energy, respectively, with 1-GB memory, compared with an energy-efficient multicore scheduling scheme. Larger energy reduction can be further achieved with larger size of memory.

In this paper, we propose the optional preference model for the facility location game with two heterogeneous facilities on a line. Agents in this new model are allowed to have optional preference, which gives more flexibility for agents to report. Aiming at minimizing maximum cost or sum cost of agents, we propose different deterministic strategy-proof mechanisms without monetary transfers. Depending on which facility the agent with optional preference cares for, we consider two variants of the optional preference model: Min (caring for the closer one) and Max (caring for the further one). For the Min variant, we propose a 2-approximation mechanism for the maximum cost objective, as well as a lower bound of 4/3, and a (n/2+1)-approximation mechanism for the sum cost objective, as well as a lower bound of 2. For Max variant, we propose an optimal mechanism for the maximum cost objective and a 2-approximation mechanism for the sum cost objective.

Cloud computing platforms enable applications to offer low latency access to user data by offering storage services in several geographically distributed data centers. In this paper, we identify the high tail latency problem in cloud CDN via analyzing a large-scale dataset collected from 783,944 users in a major cloud CDN. We find that the data downloading latency in cloud CDN is highly variable, which may significantly degrade the user experience of applications. To address the problem, we present TailCutter, a workload scheduling mechanism that aims at optimizing the tail latency while meeting the cost constraint given by application providers. We further design the Maximum Tail Minimization Algorithm (MTMA) working in TailCutter mechanism to optimally solve the Tail Latency Minimization (TLM) problem in polynomial time. We implement TailCutter across data centers of Amazon S3 and Microsoft Azure. Our extensive evaluation using large-scale real world data traces shows that TailCutter can reduce up to 68% 99th percentile user-perceived latency in comparison with alternative solutions under cost constraints.

The rapid development of the Internet of Things (IoT) has increased the requirement on the processing capabilities of sensors, mobile phones and smart devices. Meanwhile, energy efficiency techniques are in desperate need as most devices in the IoT systems are battery powered. Following the above two trends, this work explores the memory system energy efficiency for a general multi-core architecture. This architecture integrates a local memory in each processing core, with a large off-chip memory shared among multiple cores. Decisions need to be made on whether tasks will be executed with the shared memory or the local memory to minimize the total energy consumption within real-time constraints. This paper proposes optimal schemes as well as a polynomial-time approximation algorithm with constant ratio. The complexity analysis of the problem for different task and system models is also presented. Experimental results show that the proposed approximation algorithm performs close to the optimal solution in average.

In a participatory sensing system, data sensed from smartphone users are shared with the general public who requests data through submitting tasks. When multiple tasks request the data from a mobile user, the mobile user can make a transmission schedule to achieve the balance between the amount of data transmitted and energy consumption. Intuitively, reducing the amount of data transmitted by making use of data sharing between the tasks can save the energy consumption. However, due to the convexity of rate-power function for rate-adaptive transmitting devices, a schedule purely minimizing the amount of data transmitted may not always be the optimal one minimizing the energy consumption. Thus, there exists a tradeoff between the amount of data transmitted and energy consumption. This paper formulates the problem as a bi-objective optimization problem to simultaneously minimize the amount of data transmitted and the energy consumption. Two task models are studied, first-in-first-out (FIFO) task model and arbitrary deadline (AD) task model, respectively. We first provide optimal algorithms for the off-line case. We then study the online case where requests arrive dynamically without prior information. For FIFO tasks, we develop an online algorithm that is O(ln L)-competitive with respect to both the amount of data transmitted and energy consumption, where L is the longest length of the time duration of the tasks. For AD tasks, we devise an online algorithm that is O(ln2L)-competitive with respect to both the amount of data transmitted and energy consumption. Our simulation results validate the efficiency of our online algorithms.

With the booming cloud computing industry, computational resources are readily and elastically available to the customers. In order to attract customers with various demands, most Infrastructure-as-a-service (IaaS) cloud service providers offer several pricing strategies such as pay as you go, pay less per unit when you use more (so called volume discount), and pay even less when you reserve. The diverse pricing schemes among different IaaS service providers or even in the same provider form a complex economic landscape that nurtures the market of cloud brokers. By strategically scheduling multiple customers' resource requests, a cloud broker can fully take advantage of the discounts offered by cloud service providers. In this paper, we focus on how a broker can help a group of customers to fully utilize the volume discount pricing strategy offered by cloud service providers through cost-efficient online resource scheduling. We present a randomized online stack-centric scheduling algorithm (ROSA) and theoretically prove the lower bound of its competitive ratio. Three special cases of the offline concave cost scheduling problem and the corresponding optimal algorithms are introduced. Our simulation shows that ROSA achieves a competitive ratio close to the theoretical lower bound under the special cases. Trace-driven simulation using Google cluster data demonstrates that ROSA is superior to the conventional online scheduling algorithms in terms of cost saving.

We study the problem of locating a single facility on a real line based on the reports of self-interested agents, when agents have double-peaked preferences, with the peaks being on opposite sides of their locations.We observe that double-peaked preferences capture real-life scenarios and thus complement the well-studied notion of single-peaked preferences. We mainly focus on the case where peaks are equidistant from the agents’ locations and discuss how our results extend to more general settings. We show that most of the results for single-peaked preferences do not directly apply to this setting; this makes the problem essentially more challenging. As our main contribution, we present a simple truthful-in-expectation mechanism that achieves an approximation ratio of 1+b/c for both the social and the maximum cost, where b is the distance of the agent from the peak and c is the minimum cost of an agent. For the latter case, we provide a 3/2 lower bound on the approximation ratio of any truthful-in-expectation mechanism. We also study deterministic mechanisms under some natural conditions, proving lower bounds and approximation guarantees. We prove that among a large class of reasonable mechanisms, there is no deterministic mechanism that outpeforms our truthful-in-expectation mechanism.

In a wireless system, when multiple applications can share data transmitted by rate-adaptive wireless devices, there exists a trade-off between transmission redundancy and energy efficiency. This paper conducts the first theoretical analysis on such a trade-off. We formulate the problem as a bi-objective optimization problem to simultaneously minimize the transmission redundancy and the energy consumption. In the offline setting that the full information is known in advance, we provide optimal algorithms for the bi-objective optimization problem. In the online setting, we provide an online algorithm with proven performance bound to approximate the optimal solution without relying on any assumed distribution or future information. The proposed online algorithm is proved O(ln T)-competitive with respect to transmission redundancy and also O(ln T)-competitive with respect to energy consumption, where T is the number of time slots. That is, the output of the algorithm always approximates the optimal solution within a logarithmic factor over all possible inputs. Our simulation results further validate the efficiency of our online algorithm.

This paper presents an optimal rate scheduling algorithm called Truncation for an energy-harvesting enabled wireless transmitter to transmit a set of dynamically arrived packets with minimum transmission energy. Distinct from existing works, we allow packets to have individual delay constraints, which is the most general model ever assumed but is very much desired to guarantee per-application quality-of-service (QoS). Moreover, we restrict the allowable rates to a set of discrete values, which is more practical and required in many real applications. As the first achievement, we obtain an optimal offline algorithm, which assumes the rate is continuously adjustable. Then, we propose a general framework that transforms any algorithm using the continuous-rate model into an algorithm using only discrete-rates, while preserving the optimality as long as the optimality holds for convex rate-power functions. It is possible that the harvested energy is insufficient to guarantee all packets to meet their deadlines. Should this occur, maximizing throughput with the limited available energy becomes the goal to achieve. Our Truncation algorithm is able to identify this case and produces a schedule that guarantees maximum throughput, if packets share a common deadline. Furthermore, based on the optimal offline algorithms, an efficient online algorithm is designed which has been shown by simulations to produce near optimal results.

Multi-hop coverage extension can be utilized as a feasible approach to facilitating uncovered users to get Internet service in public area WLANs. In this paper we introduce a relay-union network (RUN), which refers to a public area WLAN in which users often wander in the same area and have the ability to provide data forwarding services for others. We develop a RUN framework to model the cost of providing forwarding services and the utility obtained by gaining services. The objective of the RUN is to maximize the total Quality of Cooperation (QoC) of users in the RUN. Two optimal bandwidth allocation schemes are proposed for both free and dynamic bandwidth demand models. To make our scheme more pragmatic, we then consider a more practical scenario in which the bandwidth capacity of the relays and the minimum demand of the clients are bounded. We prove that the problems under both the single relay and the multi-relay scenario are NP-hard. Three heuristic algorithms are proposed to deal with bandwidth allocation and relay-client association. We also propose a distributed signaling protocol and divide the centralized MRMC algorithm into three distributed ones to better adapt for real network environment. Finally, extensive simulations demonstrate that our RUN framework can significantly improve the efficiency of cooperation in the long term.

Efficient and effective system-level power management for multi-core systems with multiple voltage islands is necessary for next-generation computing systems. This paper considers energy efficiency for such systems, in which the cores in the same voltage island have to be operated at the same supply voltage level. We explore how to map given task sets onto cores, so that each task set is assigned and executed on one core and the energy consumption is minimized. Due to the restriction to operate at the same supply voltage in a voltage island, different mappings will result in different energy consumptions. By using the simple single frequency approximation scheme (SFA) to decide the voltages and frequencies of individual voltage islands, this paper presents the approximation factor analysis (in terms of energy consumption) for simple heuristic algorithms, and develops a dynamic programming algorithm, which derives optimal mapping solutions for energy minimization when using SFA. We experimentally evaluate the running time and energy consumption performance of these algorithms on Intel's single-chip cloud computer (SCC). Moreover, we conduct simulations for hypothetical platforms with different number of voltage islands and cores per island, also considering different task partitioning policies.

In cellular networks, it is important to conserve energy while at the same time ensuring users to have good transmission experiences. The energy cost can result from tail energy due to the radio resource control strategies designed in cellular networks and data transmission. Existing efforts generally consider one of the energy issues, and also ignore the adverse impact on user transmission performance due to energy conservation. In addition, many existing algorithms are based on prediction and knowledge on future traffic, which are hard to apply in a practical wireless system with dynamic user traffic and channel condition. The goal of this work is to design an efficient online scheduling algorithm to minimize energy consumption both due to tail energy and transmissions while meeting user performance expectation. We prove the problem to be NP-hard, and design a practical online scheduling algorithm PerES to minimize the total energy cost of multiple mobile applications subject to user performance constraints. We propose a comprehensive performance cost metric to capture the impacts due to task delay, deadline violation, different application profiles and user preferences. We prove that our proposed scheduling algorithm can make the energy consumption arbitrarily close to that of the optimal scheduling solution. The evaluation results demonstrate the effectiveness of our scheme and its higher performance than peers. Moreover, by supporting dynamic performance requirement by mobile users, PerES can achieve 2 times faster convergence to both the performance degradation bound and optimal energy conversation bound than those of traditional static methods. Using 821 million traffic flows collected from a commercial cellular carrier, we verify our scheme could achieve on average 32%-56% energy savings with different levels of user experience.

This paper presents a quantitative study on the energy-traffic tradeoff problem from the perspective of entire Wireless Local Area Network (WLAN). We propose a novel Energy-Efficient Cooperative Offloading Model (E2COM) for energy-traffic tradeoff, which can ensure the fairness of energy consumption of mobile devices and reduce the computation repetition and eliminate the Internet data traffic redundancy through cooperative execution and sharing computation results. We design an Online Task Scheduling Algorithm (OTS) based on a pricing mechanism and Lyapunov optimization to address the problem without predicting future information on task arrivals, transmission rates and so on. OTS can achieve a desirable tradeoff between the energy consumption and Internet data traffic by appropriately setting the tradeoff coefficient. Simulation results demonstrate that E2COM is more efficient than no offloading and cloud offloading for a variety of typical mobile devices, applications and link qualities in WLAN.

Wi-Fi networks have enjoyed an unprecedent penetration rate in recent years. However, due to the limited coverage, existing Wi-Fi infrastructure only provides intermittent connectivity for mobile users. Once leaving the current network coverage, Wi-Fi clients must actively discover new Wi-Fi access points (APs), which wastes the precious energy of mobile devices. Although several solutions have been proposed to address this issue, they either require significant modifications to existing network infrastructures or rely on context information that is not available in unknown environments. In this work, we develop a system called ZiFithat utilizes ZigBee radios to identify the existence of Wi-Fi networks through unique interference signatures generated by Wi-Fi beacons. We develop a new digital signal processing algorithm called common multiple folding (CMF) that accurately amplifies periodic beacons in Wi-Fi interference signals. ZiFi also adopts a constant false alarm rate (CFAR) detector that can minimize the false negative (FN) rate of Wi-Fi beacon detection while satisfying the user-specified upper bound on false positive (FP) rate. We have implemented ZiFi on two platforms, a Linux netbook integrating a TelosB mote through the USB interface, and a Nokia N73 smartphone integrating a ZigBee card through the miniSD interface. Our experiments show that, under typical settings, ZiFi can detect Wi-Fi APs with high accuracy (<;5 percent total FP and FN rate), short delay (~780 ms), and little computation overhead.

One of the most fundamental tasks of wireless sensor networks is to provide coverage of the deployment region. We study the coverage of a line interval with a set of wireless sensors with adjustable coverage ranges. Each coverage range of a sensor is an interval centered at that sensor whose length is decided by the power the sensor chooses. The objective is to find a range assignment with the minimum cost. There are two variants of the optimization problem. In the discrete variant, each sensor can only choose from a finite set of powers, whereas in the continuous variant, each sensor can choose power from a given interval. For the discrete variant of the problem, a polynomial-time exact algorithm is designed. For the continuous variant of the problem, NP-hardness of the problem is proved and followed by an ILP formulation. Then, constant-approximation algorithms are designed when the cost for all sensors is proportional to r κ for some constant κ ≥ 1, where r is the covering radius corresponding to the chosen power. Specifically, if κ = 1, we give a 1.25-approximation algorithm and a fully polynomial-time approximation scheme; if κ > 1, we give a 2-approximation algorithm. We also show that the approximation analyses are tight.

Maximizing the wireless network capacity under physical interference model is notoriously hard due to the nonlocality and the additive nature of the wireless interference under the physical interference model. This problem has been extensively studied recently with the achievable approximation bounds progressively improved from the linear factor to logarithmic factor. It has been a major open problem whether there exists a constant-approximation approximation algorithm for maximizing the wireless network capacity under the physical interference model. In this paper, we improve the status quo for the case of linear transmission power assignment, which is widely adopted due to its advantage of energy conservation. By exploring and exploiting the rich nature of the wireless interference with the linear power assignment, we develop constant-approximation algorithms for maximizing the wireless network capacity with linear transmission power assignment under the physical interference model, in both the unidirectional mode and the bidirectional mode.

Lack of proper maintenance is the root cause of anywhere from a third to a half of downtime events in a cloud data center. To help safeguard the uptime of data centers, regular preventive maintenance must be conducted. During the maintenance time, some accommodated virtual machines (VMs) may be re-provisioned to the other available (backup) resource through migration, and some VMs may be terminated. One way that can allow a data center to perform all necessary preventive maintenance activities without causing too much disruption to VMs is to design an appropriate maintenance schedule. In this paper, given the available resource in a data center and the required maintenance activities with their deadlines, we consider the joint VM resource provisioning and maintenance scheduling problem to maximize the revenue of the data center. We tackle the problem by firstly proposing a heuristic for the resource provisioning under a given maintenance schedule. Using such a heuristic algorithm as the building block, we then propose another heuristic algorithm to solve the joint resource provisioning and maintenance scheduling problem and also derive its upper bound. Extensive simulations have shown that our proposed heuristic algorithms can effectively maximize the revenue of the data center.

We propose a novel architecture of data center networks (DCN), which adds wireless network card to both servers and routers. Existing traffic redundancy elimination (TRE) mechanisms reduce link loads and increase network capacity in several environments by removing strings that have appeared in earlier packets through encoding and decoding them several hops downstream. This article is the first to explore TRE mechanisms in large-scale DCNs and the first to exploit cooperative TRE among servers. Moreover, it also achieves the `logically centralized' control over the physically distributed states in emerging software defined networks (SDN) paradigm, by sharing information among servers and routers in data centers with wireless cards. We first formulate the TREDaCeN (TRE in Data Center Networks) problem and reduce the cycle cover problem to prove that finding an optimal caching task assignment for TREDaCeN problem is NP-hard. We further describe an offline TREDaCeN algorithm which is proved to have good approximation ratio. We then discuss efficient online zero-delay and semi-distributed implementations of TREDaCeN supported by physical proximity of servers and routers, enabling status updates in a single wireless transmission, using an efficient prioritized schedule. We also address online cache replacement and consistency of information in servers and routers with and without delay. Our framework is tested on different parameters and shows superior performance in comparison to other mechanisms (imported directly to this setting). Our results show the robustness and the trade-off between the `logically centralized' implementation and the overhead on handling inconsistency of distributed information in DCN.

Energy and thermal issues are two important concerns for embedded system design. Diminished energy dissipation leads to a longer battery life, while reduced temperature hotspots decelerate the physical failure mechanisms. The instruction fetch logic associated with register access has a significant contribution towards the total energy consumption. Meanwhile, the register file has also been previously shown to exhibit the highest temperature compared to the rest of the components in an embedded processor. Therefore, the optimization of energy and the resolution of the thermal issue for register accesses are of great significance. In this article, register allocation techniques are studied to simultaneously reduce energy consumption and heat buildup on register accesses for embedded systems. Contrary to prevailing intuition, we observe that optimizing energy and optimizing temperature on register accesses conflict with each other. We introduce a rotator hardware in the instruction decoder to facilitate a balanced solution for the two conflicting objectives. Algorithms for register allocation and refinement are proposed based on the access patterns and the effects of the rotator. Experimental results show that the proposed algorithms obtain notable improvements of energy and peak temperature for embedded applications.

About 55% of all CPUs sold in the world are 8-bit microcontrollers or microprocessors which can only access limited memory space without extending address buses. Partitioned memory with bank switching is a technique to increase memory size without extending address buses. Bank Selection Instructions (BSLs) need to be inserted into the original programs to modify the bank register to point to the desired banks. These BSLs introduce both code size and execution time overheads. In this paper, we partition variables into different banks and insert BSLs at different positions of programs so that the overheads can be minimized. Minimizing speed (execution time) overhead and minimizing space (code size) overhead are two objectives investigated in this paper. A multi-copy approach is also proposed to store multiple copies of several variables on different banks when the memory space allows. It takes the read/write properties of variables into consideration and achieves more BSL overhead reduction. Experiments show that the proposed algorithms can reduce BSL overheads effectively compared to state-of-the-art techniques.

In this paper, we consider the task allocation problem on a hybrid main memory composed of nonvolatile memory (NVM) and dynamic random access memory (DRAM). Compared to the conventional memory technology DRAM, the emerging NVM has excellent energy performance since it consumes orders of magnitude less leakage power. On the other hand, most types of NVMs come with the disadvantages of much shorter write endurance and longer write latency as opposed to DRAM. By leveraging the energy efficiency of NVM and long write endurance of DRAM, this paper explores task allocation techniques on hybrid memory for multiple objectives such as minimizing the energy consumption, extending the lifetime, and minimizing the memory size. The contributions of this paper are twofold. First, we design the integer linear programming (ILP) formulations that can solve different objectives optimally. Then, we propose two sets of heuristic algorithms including three polynomial time offline heuristics and three online heuristics. Experiments show that compared to the optimal solutions generated by the ILP formulations, the offline heuristics can produce near-optimal results.

In multi-hop wireless networks where links are prone to be broken or degraded, it is important to guarantee the network connectivity as well as satisfy the performance requirements. Observing the promising features of Multiple-Input Multiple-Output (MIMO) techniques for improving the transmission capacity and reliability, in this paper, we make the very first attempt to deploy MIMO nodes as relays to assist weak links in wireless networks, with the aim of reducing the number of relay nodes and providing performance provisioning. We identify the specific constraints of MIMO relay nodes for assisting weak links, and take advantage of the MIMO ability to flexibly select among different transmission strategies. The constrains and flexibility, however, make the MIMO deployment problem different from conventional single-antenna deployment schemes and much more challenging. Based on the constraints, we formulate the MIMO relay deployment problem, and provide a polynomial-time approximation scheme (PTAS) algorithm, as well as a distributed heuristic algorithm. The performance of the proposed algorithms is evaluated through simulations and demonstrated to be very effective.

Protecting networking infrastructures from malicious attacks is important as a successful attack on a high data rate link can cause the loss or delay of large amounts of data. In this paper, we consider a proactive approach where the ISPs are willing to allocate some (limited) resources to defend the networking infrastructures against the attacks. We aim to answer where and how much the defending resource should be placed so that the expected data loss can be minimized no matter where the attacker may launch the attack. We model the problem as a 2-player zero-sum game where the payoffs are measured by the maximum network flow. In order to overcome the unique challenges of such payoffs, we transform the payoffs into explicit piece-wise functions through multi-parametric linear programming (MP-LP) and divide the entire strategy space into a set of critical regions. We prove that a global Nash Equilibrium (NE) exists when there is only one critical region. However, when the number of critical regions is greater than 1, there is no global NE. We also prove that there exists one and only one local NE in each critical region. We then design a mixed-strategy solution. Our results have shown that to dedicate all defending resources to one min-cut set when there are multiple min-cut sets will not be an optimal solution, however, min-cut strategies will have higher probabilities to be selected in the mixed-strategy solution when the defending resource is limited.

Owing to its potential to satisfy all outstanding requests for the same data item with a single response, on-demand data broadcast becomes a widely accepted approach to dynamic and scalable wireless information dissemination. In some emerging applications, such as road traffic navigation system, users prefer to request multiple dependent data items at a time. In addition, requests usually have deadline constraints for real-time applications. However, in existing works, clients will not know that their requests cannot be satisfied until the deadlines expire. In this paper, admission control is introduced to data broadcast systems such that clients can be informed in advance in the case that their requests have no hope to be satisfied so that earlier remedial actions can be taken. Furthermore, a matching based allocation scheme is proposed to maximize data sharing among requests in multi-channel architectures. Simulation results show that our proposed algorithms have better performance and quality of service (QoS) than traditional algorithms.

Recent research shows that significant energy saving can be achieved in mobility-enabled wireless sensor networks (WSNs) that visit sensor nodes and collect data from them via short-range communications. However, a major performance bottleneck of such WSNs is the significantly increased latency in data collection due to the low movement speed of mobile base stations. To address this issue, we propose a rendezvous-based data collection approach in which a subset of nodes serve as rendezvous points that buffer and aggregate data originated from sources and transfer to the base station when it arrives. This approach combines the advantages of controlled mobility and in-network data caching and can achieve a desirable balance between network energy saving and data collection delay. We propose efficient rendezvous design algorithms with provable performance bounds for mobile base stations with variable and fixed tracks, respectively. The effectiveness of our approach is validated through both theoretical analysis and extensive simulations.

In this paper, we utilize a hybrid main memory composed of DRAM and Phase Change Random Access Memory (PRAM) for DSP systems, which leverages the low power consumption of PRAM while minimizing the performance and endurance degradation caused by write operations on PRAM. We re-consider the variable partitioning problem on this hybrid main memory. Different objectives, for example power consumption and the number of writes on PRAM, are considered in this paper. By using the proposed models and algorithms, experiments show that we can reduce 53% power consumption and 79% the number of writes on PRAM on average, compared with pure DRAM and pure PRAM memory, respectively.

In this paper, we focus on register allocation techniques to simultaneously reduce energy consumption and heat buildup of register accesses. The conflict between these two objectives is resolved through the introduction of a hardware rotator. A register allocation algorithm followed by a refinement method is proposed based on the access patterns and the effects of the rotator. Experimental results show that the proposed algorithms obtain notable improvements in energy consumption and temperature reduction for embedded applications.

Longest Queue First (LQF) is a well-known link scheduling strategy in multihop wireless networks. Its throughput efficiency ratio was shown to be exactly the local pooling factor (LPF) of the multihop wireless network in a recent seminar work by Joo et al.. Under the 802.11 interference model with uniform interference radii, the LPF of a multihop wireless network was known to be at least 1/6. However, little is known about the LPF of a multihop wireless network under the 802.11 interference model with arbitrary interference radii or under the protocol interference model. In this paper, we derive constant lower bounds on LPFs of these multihop wireless networks. Specifically, under the 802.11 interference model with arbitrary interference radii, the LPF is at least 1/16. Under the protocol interference model, if the communication radius of each node is at most c times its interference radius for some c <; 1, then the LPF is at least 1/ (2 ⌈π/ arcsin 1-c/2⌈ - 1)).

Link scheduling is a fundamental design issue in multihop wireless networks. All existing link scheduling algorithms require the precise information of the positions, and/or communication/interference radii of all nodes. For practical networks, it is not only difficult or expensive to obtain these parameters, but also often impossible to get their precise values. The link scheduling determined by the imprecise values of these parameters may fail to guarantee the same approximation bounds of the link scheduling determined by precise values. Therefore, the existing link scheduling algorithms lack performance robustness. In this paper, we propose a robust link scheduling, which can be easily computed with only the information on whether a given pair of links have conflict or not and therefore is robust. In addition, our link scheduling does not compromise the approximation bound and indeed sometimes can achieve better approximation bound. Particularly, under the 802.11 interference model, its approximation bound is 16 in general and 6 with uniform interference radii, an improvement over the respective best-known approximation bounds 23 and 7.

We present a fault-tolerant post-mapping resynthesis for FPGA-based designs that exploits the dual-output feature of modern FPGA architectures to improve the reliability of a mapped circuit against faults. Emerging FPGA architectures, such as 6-LUTs in Xilinx Virtex-5 and 8-input ALMs in Altera Stratix-III, have a secondary LUT output that allows access to non-occupied SRAM bits. We show that this architectural feature can be used to build redundancy for fault masking with limited area and performance overhead. Our algorithm improves reliability of a mapping by performing two basic operations: duplication (in which free configuration bits are used to duplicate a logic function whose value is obtained at the secondary output) and encoding (in which two copies of the same logic function are ANDed or ORed together in the fanout of the duplicated logic). The problem of fault tolerant post-mapping resynthesis is then formulated as the optimal duplication and encoding scheme that ensures the minimal circuit fault rate w.r.t. a stochastic single fault model. We present an ILP formulation of this problem and an efficient algorithm based on generalized network flow. On MCNC benchmarks, experimental results show that for combinational circuits the proposed approach improves mean-time-to-failure(MTTF) by 27% with 4% area overhead, and the proposed approach with explicit area redundancy improves MTTF by 113% with 36% area overhead, compared to the baseline mapping by ABC. This provides a viable fault tolerance solution for non-mission critical applications compared to TMR (triple modular redundancy) which has a 5x–6x area overhead.

Multiple memory banks with bank switching is a technique to increase memory size without extending address buses. A special instruction, Bank Selection Instruction (BSL) is inserted into the original programs to modify the bank register to point to the right bank, which increases both the code size and runtime overhead. In this paper, we carefully partition variables into different banks and insert BSLs at different positions so that the overheads can be minimized. Minimizing code size and minimizing runtime overhead are two objectives investigated in this paper. Experiments show that the algorithms proposed can reduce the overhead caused by BSLs efficiently.

Cache is known for its unpredictability in embedded systems. Cache locking technique is often utilized to guarantee a tighter prediction of Worst-Case Execution Time (WCET) which is one of the most important performance metrics for embedded systems. However, in Multi-Processor Systems-on-Chip (MPSoC) systems with multi-tasks, Level 2 (L2) cache is often shared among different tasks and cores, which leads to higher complexity in the cache management and extended unpredictability of cache. Task assignment has inherent relevancy for cache behavior, while cache behavior also affects the efficiency of task assignment. Task assignment and cache behavior have dramatic influences on the overall WCET of MPSoC. In this paper, overall WCET represents the worst-case finishing time of a set of tasks running on different cores. This paper proposes joint task assignment and cache partitioning techniques to minimize the overall WCET for MPSoC systems. Cache locking is applied to each task to guarantee a precise WCET, which in return facilitates task assignment and cache partitioning. We prove that the joint problem is NP-Hard and propose several efficient algorithms. Experimental results show that the proposed algorithms can consistently reduce the overall WCET compared to previous techniques.

The capacity region of multihop wireless network is involved in many capacity optimization problems. However, the membership of the capacity region is NP-complete in general, and hence the direct application of capacity region is quite limited. As a compromise, we often substitute the capacity region with a polynomial approximate capacity subregion. In this paper, we construct polynomial ¿-approximate capacity subregions of multihop wireless network under either 802.11 interference model or protocol interference model in which all nodes have uniform communication radii normalized to one and uniform interference radii ¿ ¿ 1. The approximation factor ¿ decreases with ¿ in general and is smaller than the best-known ones in the literature. For example, ¿ = 3 when ¿ ¿ 2.2907 under the 802.11 interference model or when ¿ ¿ 4.2462 under the protocol interference model. Our construction exploits a nature of the wireless interference called strip-wise transitivity of independence discovered in this paper and utilize the independence polytopes of cocomparability graphs in a spatial-divide-conquer manner. We also apply these polynomial ¿-approximate capacity subregions to compute ¿-approximate solutions for maximum (concurrent) multiflows.

A large number of embedded systems include 8-bit microcontrollers for their energy efficiency and low cost. Multi-bank memory architecture is commonly applied in 8-bit microcontrollers to increase the size of memory without extending address buses. To switch among different memory banks, a special instruction, Bank Selection, is used. How to minimize the number of bank selection instructions inserted is important to reduce code size for embedded systems.

Recent years have witnessed the emergence of numerous new Internet services for mobile users. Supporting mobile applications via public WiFi networks has received significant research attention due to the drastic increase of penetration rate of 802.11-based networks. Nevertheless, recent empirical studies showed that unplanned WiFi networks cannot provide satisfactory Quality of Service for interactive mobile applications due to intermittent network connectivity. In this paper, we exploit realistic mobility characteristics of users to deploy WiFi Access Points (APs) for continuous service for mobile users. We study two AP deployment problems that aim to maximize the continuous user coverage and to minimize the AP deployment cost, respectively. Both problems are formulated based on mobility graphs that capture the statistical mobility patterns of users. We prove that both problems are NP-hard. We develop several optimal and approximation algorithms with provable performance bounds for different topologies of mobility graphs. The effectiveness of our approaches is validated by extensive simulations using real user mobility traces.

VLIW architectures have gained acceptance in embedded systems. Traditional monolithic register file is not suitable for VLIW architectures with a large number of functional units. Clustered VLIW architecture is often applied, where the register file is partitioned into a number of smaller register files. Register files represent a substantial portion of the energy consumption in modern processors, and it is growing rapidly with wider instruction width. Most of the known clustered VLIW architectures partition the register file evenly among clusters. In this paper, we study the effect of energy consumption with register file re-partitioning on clustered VLIW architecture, where register files are not necessarily partitioned evenly. We present algorithms to compute energy-efficient re-partition of register files under different conditions. The impact of different intercluster communication models as well as the impact of program behavior on the register file re-partitioning are analyzed in this paper. Experimental results show that energy saving can be achieved using the proposed techniques.

Cache is effective in bridging the gap between processor and memory speed. It is also a source of unpredictability because of its dynamic and adaptive behavior. Worst-case execution time (WCET) of an application is one of the most important criteria for real-time embedded system design. The unpredictability of instruction miss/hit behavior in the instruction cache (I-Cache) leads to an unnecessary over-estimation of the real-time application's WCET. A lot of modern processors provide cache locking capability. Static I-Cache locking locks function/instruction blocks of a program into the I-Cache before program execution. In this way, a more precise estimation of WCET can be achieved. The selection of functions/instructions to be locked in the I-Cache has dramatic influence on the performance of the real-time application. This paper focuses on the static I-Cache locking problem to minimize WCET for real-time embedded systems. We formulate the problem using an Execution Flow Tree (EFT) and a linear programming model. For a subset of the problems with certain properties, corresponding polynomial time optimal algorithms are proposed. We prove that the general problem is an NP-Hard problem. We also show that for a subset of the general problem with certain patterns, optimal solutions can be achieved in polynomial time. Experimental results show that our algorithms can reduce the WCET of applications further compared to current best known techniques.

Modern processors often provide cache locking capability which can be applied statically and dynamically to manage cache in a predictable manner. The selection of instructions to be locked in the instruction cache (I-Cache) has dramatic influence on the performance of multi-task real-time embedded systems. This paper focuses on using cache locking techniques on a shared I-Cache in a real-time embedded system with multi-tasks to minimize its worst-case utilization (WCU) which is one of the most important criteria for designing realtime embedded systems. We analyze the static and dynamic strategies to perform I-Cache locking and propose different algorithms which utilize the fore knowing information of the real-time embedded applications. Experiments show that the proposed algorithms can reduce WCU further compared to previous techniques. Design suggestions on which strategy should be utilized under different situations are also induced from the experimental results.

Recent years have seen the deployments of wireless sensor networks (WSNs) in a variety of applications to gather the information about physical environments. A key requirement of many data-gathering WSNs is to deliver the information about dynamic physical phenomena to users at multiple temporal resolutions. In this paper, we propose a novel solution called theMinimumIncrementalDisseminationTree(MIDT) for dynamic multiresolution data dissemination in WSNs. MIDT includes an online tree construction algorithm with an analytical performance bound and two lightweight tree adaptation heuristics for handling data requests with dynamic temporal resolutions. Our simulations based on realistic settings of Mica2 motes show that MIDT outperforms several typical data dissemination schemes. The two tree adaptation heuristics can effectively maintain desirable energy efficiency of the dissemination tree while reducing the overhead of tree reconfigurations under representative traffic patterns in WSNs.

Recent research shows that significant energy saving can be achieved in wireless sensor networks with a mobile base station that collects data from sensor nodes via short-range communications. However, a major performance bottleneck of such WSNs is the significantly increased latency in data collection due to the low movement speed of mobile base stations. To address this issue, we propose a rendezvous-based data collection approach in which a subset of nodes serve as the rendezvous points that buffer and aggregate data originated from sources and transfer to the base station when it arrives. This approach combines the advantages of controlled mobility and in-network data caching and can achieve a desirable balance between network energy saving and data collection delay. We propose two efficient rendezvous design algorithms with provable performance bounds for mobile base stations with variable and fixed tracks, respectively. The effectiveness of our approach is validated through both theoretical analysis and extensive simulations.

In a general context, the sharing of intermediate service results among different processes is seldom feasible because parameters are often different and there may be transactional and side effects. However, in a streaming video multicast environment, a large number of users often request various similar processing on the same stream. Therefore, service sharing is feasible, with a large potential of savings in processing cost. In this paper, we study the problem of determining the service invocation orders for multiple service composition requests in a streaming video multicast with the aim of maximizing the service sharing. We first formally define the problem. After proving the problem is NP-complete, we develop an optimal algorithm for the base case of two requests. Then for the general case, we develop two heuristic algorithms, namely,aglobal greedy algorithm and a local greedy algorithm using the optimal algorithm for the base case as the building block. The global greedy algorithm is designed for a system where the existing service composition requests can be recomposed with the arrival of a new request. The local greedy algorithm can be used in a system where the existing service composition requests do not change their service composition solutions with the arrival of a new request. We prove that the global greedy algorithm is a 2-approximation algorithm in terms of maximizing service sharing. Simulation results show that the greedy algorithms can save more service costs compared with a naive algorithm, and are effective compared with the cost lower bound.

Recently, several storage-centric wireless sensor networks (WSNs) have been developed to store massive sensor data in the network. A crucial task of these networks is to disseminate useful information to the users at dynamic temporal resolutions. We formulate the problem of dynamic multi-resolution data dissemination in this paper. We propose a novel solution called the Minimum Incremental Dissemination Tree (MIDT) that includes an online tree construction algorithm with analytical performance bound and two lightweight tree adaptation heuristics for handling data requests with dynamic temporal resolutions. Our simulations show that MIDT outperforms several typical data dissemination schemes. The two tree adaptation heuristics can effectively maintain desirable energy efficiency of the dissemination tree while minimizing the tree adaption overhead under representative traffic patterns in WSNs.

We investigate the key management problem for broadcasting applications. Previous work showed that batch rekeying can be more cost-effective than individual rekeying. Under the assumption that every user has probability p of being replaced by a new user during a batch rekeying period, we study the structure of the optimal key trees. Constant bounds on both the branching degree and the subtree size at any internal node are established for the optimal tree. These limits are then utilized to give an $O(n)$ dynamic programming algorithm for constructing the optimal tree for n users and any fixed value of p. In particular, we show that when $p > 1 - 3^{-1/3} \thickapprox 0.307$, the optimal tree is an n-star, and when $p\leq 1 - 3^{-1/3}$, each nonroot internal node has a branching degree of at most 4. We also study the case when p tends to 0 and show that the optimal tree resembles a balanced ternary tree to varying degrees depending on certain number-theoretical properties of n.

We consider the problem of job scheduling on a variable voltage processor with d discrete voltage/speed levels. We give an algorithm which constructs a minimum energy schedule for n jobs in $O(d n\log n)$ time. Previous approaches solve this problem by first computing the optimal continuous solution in $O(n^3)$ time and then adjusting the speed to discrete levels. In our approach, the optimal discrete solution is characterized and computed directly from the inputs. We also show that $O(n\log n)$ time is required; hence the algorithm is optimal for fixed d.