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 .

By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers mainly focus on end-to-end solution learning, which suffers from the scalability issue due to the high dimensionality of the solution space. Instead of directly learning the optimal solution, this paper aims to learn a reduced and equivalent model of the original MILP as an intermediate step. The reduced model often corresponds to interpretable operations and is much simpler, enabling us to solve large-scale MILP problems much faster than existing commercial solvers. However, current approaches rely only on the optimal reduced model, overlooking the significant preference information of all reduced models. To address this issue, this paper proposes a preference-based model reduction learning method, which considers the relative performance (i.e., objective cost and constraint feasibility) of all reduced models on each MILP instance as preferences. We also introduce an attention mechanism to capture and represent preference information, which helps improve the performance of model reduction learning tasks. Moreover, we propose a SetCover based pruning method to control the number of reduced models (i.e., labels), thereby simplifying the learning process. Evaluation on real-world MILP problems shows that 1) compared to the state-of-the-art model reduction ML methods, our method obtains nearly 20% improvement on solution accuracy, and 2) compared to the commercial solver Gurobi, two to four orders of magnitude speedups are achieved.

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.

This work studies the challenge of scheduling real-time control commands in Networked Control Systems (NCS), where control actions rely on the freshness of data collected from multiple sources. In dynamic environments, ensuring that control commands in an NCS are accurate and frequent is essential for maintaining the system responsiveness. For this aim, we introduce a new metric, Age of Result (AoR), which quantifies the time elapsed since the last control command was generated and executed. This metric reflects the system’s capability to adapt to real-time changes in the operational environment by considering both data freshness and control command frequency. We conduct a detailed analysis of AoR in NCS, paying special attention to the dependencies between sensing and computing phases. We first address computation-intensive and network-intensive scenarios, proposing random sampling (RS)-based approximate algorithms for each case. Subsequently, we develop another RS-based algorithm and a heuristic approach for the general model. Simulation results demonstrate that our approach can effectively minimize AoR and significantly enhance the system performance and real-time adaptability compared to existing strategies.

Information freshness, measured by the Age-of-Information (AoI) metric, is a crucial aspect of conventional network systems. However, the emergence of the Artificial Intelligence of Things (AIoT) introduces unique requirements for assessing information freshness, rendering the traditional AoI definition inadequate. This is because the traditional AoI metric operates under the presumption that each data packet bears equal significance. In contrast, AIoT systems must prioritize the transmission of event summaries from smart IoT devices. To promptly capture events as they occur at the sources, we propose a novel information freshness metric called Age of Event (AoE). Subsequently, we thoroughly investigate the problem of AoE-minimizing transmission scheduling. This issue presents a formidable challenge because the event occurrence pattern can be unpredictable, and more crucially, the base station only becomes aware of these occurrences post-transmission. In response, we formulate algorithms and conduct a theoretical analysis applicable to scenarios characterized by complete, zero, or partial knowledge of event occurrences. Evaluations performed on a real traffic event dataset reveal that even in the absence of complete knowledge, our algorithms exhibit competitive performance when compared against the clairvoyant benchmark and markedly outperform AoI baselines.

Mobile devices have been increasingly deployed in large-scale cyber-physical systems (CPS) to traverse the field and retrieve various data measurements from designated physical entities with stringent performance requirements. This work studies the Availability-constrained real-time Fresh Data Retrieval problem in CPS with a Speed Adjustable mobile device (AFDR-SA). The goal is to maintain the temporal validity of the real-time data with different priorities to be retrieved in the system while meeting the data availability constraints imposed by the communication range between the mobile device and the physical entities. The general case of the AFDR-SA problem is proved to be NP-hard. A dynamic programming (DP)-based optimal algorithm is proposed for a special scenario where the retrieval times of individual data items with the same priority are of the same length. For the general case where data items can have arbitrary retrieval times and different priorities, another different DP-based scheme is proposed, which is proved to be optimal given the retrieval order. A fast heuristic with low complexity is also proposed for the general problem to improve the computational efficiency. The experimental results show that the proposed schemes for the general case outperform the state-of-the-art methods and have close performance compared to the optimal solution while incurring much less computational overhead.

In many IoT applications, information needs to be gathered from multiple heterogeneous sources to the base station for real-time processing and follow-up actions. Undoubtedly, information freshness, measured by age of information (AoI), is critical in taking responsive actions. Recent studies have taken AoI into the consideration of transmission scheduling over wireless channels. However, existing studies on guaranteeing AoI either assume error-free wireless channels or priorly known link reliability, which is unrealistic. In this paper, we tackle the AoI-guaranteed transmission scheduling problem over an unreliable channel with the aim of throughput maximization, which is modelled as an AoI-Guaranteed Multi-Armed Bandit (AG-MAB) problem. Since the problem has not been studied in the literature even for the oracle case with given link reliability, we first propose an optimal stationary randomized sampling (SRS) policy for the oracle case. For the AG-MAB problem with unknown link reliability, we propose learning algorithms that meet the AoI requirements with probability 1 and incur sublinear regret compared to Oracle SRS, which can also detect the unsatisfiability of the AoI constraint and switch to the fallback policy promptly with guaranteed accuracy. Numerical results show that our algorithm outperforms the AoI-constraint-aware baselines on throughput with per-source AoI requirement guaranteed.

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.

This work studies the non-uniform multi-source data update problem for real-time monitoring systems, where a set of heterogeneous data sources transmit their updates to a Base Station (BS) through wire or wireless channel(s). The performance metric called Age of Information (AoI) - which measures the time elapsed since the last data update of each source received by the BS - is commonly used to quantify the freshness of the data updates. However, most existing work on minimizing AoI of multi-source data updates assume that all sources have a uniform size of data updates which unnecessarily reduces their applicability. This work explores a more general model where individual sources can have non-uniform sizes of data updates, and provides thorough analysis to optimize both peak and average AoI of the target system. Based on these analysis, an optimal scheme to minimize the peak AoI is first developed by guaranteeing the delivery frequency of each source proportional to the function determined by its data size. A$(2+\delta)$-approximation algorithm based on random sampling (RS) and a heuristic called Ratio-driven Maximum Age First (RMAF) are further proposed to minimize the average AoI. Our extensive experiments validate the bound of RS, and show that RMAF can achieve close performance to the lower bound of the minimum time-average AoI and outperforms the state-of-the-art schemes.

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.

Network function virtualization (NFV) is a promising virtualization technology that has the potential to significantly reduce the expenses and improve service agility. The NFV makes it possible for Internet service providers (ISPs) to employ various virtual network functions (VNFs) without installing new equipments. One of the most attractive approaches in the NFV technology is the so-called joint placement and allocation of virtual network functions (JPA-VNFs), which considers the balance between VNF investment with Quality of Services (QoS). We introduce a novel capability function to measure the potential of locating VNF instances for each server in the proposed OJPA-HS model. This model allows the servers in the network to be heterogeneous, at the same time combines and generalizes many classical JPA-VNF models. Despite its NP-hardness, we present a provable best-possible deterministic online algorithm based on dynamic programming (DP). To conquer the high complexity of DP, we propose two additional randomized heuristics, Las Vegas (LV) and Monte Carlo (MC) randomized algorithms, which perform even as good as DP with much smaller complexity. Besides, MC is a promising heuristic in practice as it has the advantage to deal with the big data environment. Extensive numerical experiments are constructed for the proposed algorithms in this article.

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 are given a set of n jobs and a single processor that can vary its speed dynamically. Each job J_j is characterized by its processing requirement (work) p_j, its release date r_j and its deadline d_j. We are also given a budget of energy E and we study the scheduling problem of maximizing the throughput (i.e. the number of jobs that are completed on time). While the preemptive energy minimization problem has been solved in polynomial time [Yao et al., FOCS'95], the complexity of the problem of maximizing the throughput remained open until now. We answer partially this question by providing a dynamic programming algorithm that solves the problem in pseudo-polynomial time. While our result shows that the problem is not strongly NP-hard, the question of whether the problem can be solved in polynomial time remains a challenging open question. Our algorithm can also be adapted for solving the weighted version of the problem where every job is associated with a weight w_j and the objective is the maximization of the sum of the weights of the jobs that are completed on time.