We study Online Convex Optimization (OCO) over a convex set $K\subseteq \mathbb R^d$, where in each round $t$ the learner selects $x_t\in K$ and then observes a convex loss $f_t:K\to[0,1]$, with the goal of minimizing regret to the best fixed decision in hindsight. We introduce a unified probing model that generalizes two recent lines of work: sublinear \emph{best-expert} queries in the experts setting, and pairwise (comparison-based) feedback available every round in OCO. In our framework, the learner has a budget of $k\le T$ \emph{pairwise probes}; on a probed round it may query two points and learn which one has smaller loss. Our main result shows that even a \emph{sublinear and noisy} probe budget can provably improve worst-case regret in the full feedback OCO regime. With $k$ $\delta$-noisy pairwise probes, we obtain: $ {\textup{\textsc{Reg}}}_T \le O\left(\min\left\{\sqrt{dT\ln T},; \frac{dT\ln T}{k|1-2\delta|}\right\}\right) $, which is tight (up to logarithmic factors in $T$) across $T$, $k$ and $\delta$. Specifically regarding the noise parameter $\delta \in [0,1]$, the regret guarantee smoothly degrades as the oracle response approaches a coin flip, i.e., $\delta$ is close to $\frac{1}{2}$. When applying the same techniques to a finite $K$ for the prediction with $d$ experts setting, the resulting rates are instead completely tight in all parameters, including $d$. Our analysis gives a streamlined treatment of pairwise probing in OCO by quantifying the benefit of probing via a variance reduction effect, combined with a second-order (variance-based) analysis of Continuous Exponential Weights.

Online advertising systems have recently transitioned to autobidding, allowing advertisers to delegate bidding decisions to automated agents. Each advertiser directs their agent to optimize an objective function subject to return-on-investment (ROI) and budget constraints. Given their practical relevance, this shift has spurred a surge of research on the liquid welfare price of anarchy (POA) of fundamental auction formats under autobidding, most notably simultaneous first-price auctions (FPA). One of the main challenges is to understand the efficiency of FPA in the presence of heterogeneous agent types. We introduce a type-dependent smoothness framework that enables a unified analysis of the POA in such complex autobidding environments. In our approach, we derive type-dependent smoothness parameters which we carefully balance to obtain POA bounds. This balancing gives rise to a POA-revealing mathematical program, which we use to determine tight bounds on the POA of coarse correlated equilibria (CCE). Our framework is versatile enough to handle heterogeneous agent types and extends to the general class of fractionally subadditive valuations. Additionally, we develop a novel reduction technique that transforms budget-constrained agents into budget-unconstrained ones. Combining this reduction technique with our smoothness framework enables us to derive tight bounds on the POA of CCE in the general hybrid agent model with both ROI and budget constraints. Among other results, our bounds uncover an intriguing threshold phenomenon showing that the POA depends intricately on the smallest and largest agent types. We also extend our study to FPAs with reserve prices, which can be interpreted as predictions of agents’ values, to further improve efficiency guarantees.

In the classical principal-agent hidden-action contract model, a principal delegates the execution of a costly task to an agent. In order to complete the task, the agent chooses an action from a set of actions, where each potential action is associated with a cost and a success probability to accomplish the task. To incentivize the agent to exert effort, the principal can commit to a contract, which is the amount of payment based on the task’s success but not on the hidden-action chosen by the agent.

A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to relax welfare efficiency and the use of approximation mechanisms. Such mechanisms in general make extensive use of the Bayesian priors. In this work, we investigate a question of increasing theoretical and practical importance: how much prior information is required to design mechanisms with near-optimal approximations?

In the random-order model for online learning, the sequence of losses is chosen upfront by an adversary and presented to the learner after a random permutation. Any random-order input is *asymptotically* equivalent to a stochastic i.i.d.~one, but, for finite times, it may exhibit significant *non-stationarity*, which can hinder the performance of stochastic learning algorithms. While algorithms for adversarial inputs naturally maintain their regret guarantees in random order, simple no-regret algorithms exist for the stochastic model that fail against random-order instances. In this paper, we propose a general procedure to adapt stochastic learning algorithms to the random-order model without substantially affecting their regret guarantees. This allows us to recover improved regret bounds for prediction with delays, bandits with switching costs, and online learning with constraints. Finally, we investigate online classification and prove that, in random order, learnability is characterized by the VC dimension rather than by the Littlestone dimension, thus providing a further separation from the general adversarial model.

The goal of recommender systems is to provide to users suggestions that match their interests, with the eventual goal of increasing their satisfaction, as measured by the number of transactions (clicks, purchases, and so forth). Often, this leads to providing recommendations that are of a particular type. For some contexts (e.g., browsing videos for information) this may be undesirable, as it may enforce the creation of filter bubbles. This is because of the existence of underlying bias in the input data of prior user actions. Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention. In this article, we consider both the densest subgraph and the \(k\) -clustering problem, two primitives that are being used by some recommender systems. We are given a coloring on the nodes, respectively the points, and aim to compute a fair solution \(S\) , consisting of a subgraph or a clustering, such that none of the colors is disparately impacted by the solution. Unfortunately, introducing fair solutions typically makes these problems substantially more difficult. Unlike the unconstrained densest subgraph problem, which is solvable in polynomial time, the fair densest subgraph problem is NP-hard even to approximate, which means that with the standard computational model it is probably impossible to solve (or even approximate it sufficiently well) in polynomial time. For \(k\) -clustering, the fairness constraints make the problem very similar to capacitated clustering, which is a notoriously hard problem to even approximate. Despite such negative premises, we are able to provide positive results in important use cases. In particular, we are able to prove that a suitable spectral embedding allows recovery of an almost optimal, fair, dense subgraph hidden in the input data, whenever one is present, a result that is further supported by experimental evidence. We also show a polynomial-time, \(2\) -approximation algorithm to the problem of fair densest subgraph, assuming that there exist only two colors and both colors occur equally often in the graph. This result turns out to be optimal assuming the small set expansion hypothesis. For fair \(k\) -clustering, we show that we can recover high quality fair clusterings effectively and efficiently. For the special case of \(k\) -median and \(k\) -center, we offer additional, fast and simple approximation algorithms as well as new hardness results. The above theoretical findings drive the design of heuristics, which we experimentally evaluate on a scenario based on real data, in which our aim is to strike a good balance between diversity and highly correlated items from Amazon co-purchasing graphs and Facebook contacts. We additionally evaluated our algorithmic solutions for the fair \(k\) -median problem through experiments on various real-world datasets.

Clairvoyant network design with deadlines or delay has been studied extensively, culminating in an O(log n)-competitive general framework, where n is the number of possible request types (Azar and Touitou, FOCS 2020). In the nonclairvoyant setting, the problem becomes much harder, as Ω(√n) lower bounds are known for certain problems (Azar et al., STOC 2017). However, no frameworks are known for the nonclairvoyant setting, and previous work focuses only on specific problems, e.g., multilevel aggregation (Le et al., SODA 2023). In this paper, we present the first nonclairvoyant frameworks for network design with deadlines or delay. These frameworks are nearly optimal: their competitive ratio is Õ(√n), which matches known lower bounds up to logarithmic factors.

In online learning, a decision maker repeatedly selects one of a set of actions, with the goal of minimizing the overall loss incurred. Following the recent line of research on algorithms endowed with additional predictive features, we revisit this problem by allowing the decision maker to acquire additional information on the actions to be selected. In particular, we study the power of \emph{best-action queries}, which reveal beforehand the identity of the best action at a given time step. In practice, predictive features may be expensive, so we allow the decision maker to issue at most $k$ such queries. We establish tight bounds on the performance any algorithm can achieve when given access to $k$ best-action queries for different types of feedback models. In particular, we prove that in the full feedback model, $k$ queries are enough to achieve an optimal regret of $\Theta(\min\{\sqrt T, \frac{T}{k}\})$. This finding highlights the significant multiplicative advantage in the regret rate achievable with even a modest (sublinear) number $k \in \Omega(\sqrt{T})$ of queries. Additionally, we study the challenging setting in which the only available feedback is obtained during the time steps corresponding to the $k$ best-action queries. There, we provide a tight regret rate of $\Theta(\min\{\frac{T}{\sqrt k},\frac{T^2}{k^2}\})$, which improves over the standard $\Theta(\frac{T}{\sqrt k})$ regret rate for label efficient prediction for $k \in \Omega(T^{2/3})$.

We study the problem of regret minimization for a single bidder in a sequence of first-price auctions where the bidder discovers the item’s value only if the auction is won. Our main contribution is a complete characterization, up to logarithmic factors, of the minimax regret in terms of the auction’s transparency, which controls the amount of information on competing bids disclosed by the auctioneer at the end of each auction. Our results hold under different assumptions (stochastic, adversarial, and their smoothed variants) on the environment generating the bidder’s valuations and competing bids. These minimax rates reveal how the interplay between transparency and the nature of the environment affects how fast one can learn to bid optimally in first-price auctions.

Abstract We study truthful mechanisms for welfare maximization in online bipartite matching. In our (multi-parameter) setting, every buyer is associated with a (possibly private) desired set of items, and has a private value for being assigned an item in her desired set. Unlike most online matching settings, where agents arrive online, in our setting the items arrive one by one in an adversarial order while the buyers are present for the entire duration of the process. This poses a significant challenge to the design of truthful mechanisms, due to the ability of buyers to strategize over future rounds. We provide an almost full picture of the competitive ratios in different scenarios, including myopic vs. non-myopic agents, tardy vs. prompt payments, and private vs. public desired sets. Among other results, we identify the frontier up to which the celebrated $$e/(e-1)$$ e / ( e - 1 ) competitive ratio for the vertex-weighted online matching of Karp, Vazirani and Vazirani extends to truthful agents and online items.

We study repeated bilateral trade where an adaptive $\sigma$-smooth adversary generates the valuations of sellers and buyers. We completely characterize the regret regimes for fixed-price mechanisms under different feedback models in the two cases where the learner can post the same or different prices to buyers and sellers. We begin by showing that, in the full-feedback scenario, the minimax regret after $T$ rounds is of order $\sqrt{T}$. Under partial feedback, any algorithm that has to post the same price to buyers and sellers suffers worst-case linear regret. However, when the learner can post two different prices at each round, we design an algorithm enjoying regret of order $T^{3/4}$, ignoring log factors. We prove that this rate is optimal by presenting a surprising $T^{3/4}$ lower bound, which is the paper's main technical contribution.

We study fully dynamic online selection problems in an adversarial/stochastic setting that includes Bayesian online selection, prophet inequalities, posted price mechanisms, and stochastic probing problems subject to combinatorial constraints. In the classical ``incremental'' version of the problem, selected elements remain active until the end of the input sequence. On the other hand, in the fully dynamic version of the problem, elements stay active for a limited time interval, and then leave. This models, for example, the online matching of tasks to workers with task/worker-dependent working times, and sequential posted pricing of perishable goods. A successful approach to online selection problems in the adversarial setting is given by the notion of Online Contention Resolution Scheme (OCRS), that uses a priori information to formulate a linear relaxation of the underlying optimization problem, whose optimal fractional solution is rounded online for any adversarial order of the input sequence. Our main contribution is providing a general method for constructing an OCRS for fully dynamic online selection problems. Then, we show how to employ such OCRS to construct no-regret algorithms in a partial information model with semi-bandit feedback and adversarial inputs.

We study repeated bilateral trade where an adaptive $\sigma$-smooth adversary generates the valuations of sellers and buyers. We provide a complete characterization of the regret regimes for fixed-price mechanisms under different feedback models in the two cases where the learner can post either the same or different prices to buyers and sellers.We begin by showing that the minimax regret after $T$ rounds is of order $\sqrt{T}$ in the full-feedback scenario. Under partial feedback, any algorithm that has to post the same price to buyers and sellers suffers worst-case linear regret. However, when the learner can post two different prices at each round, we design an algorithm enjoying regret of order $T^{3/4}$ ignoring log factors.We prove that this rate is optimal by presenting a surprising $T^{3/4}$ lower bound, which is the main technical contribution of the paper.

Fair allocation of indivisible goods has attracted extensive attention over the last two decades, yielding numerous elegant algorithmic results and producing challenging open questions. The problem becomes much harder in the presence of strategic agents. Ideally, one would want to design truthful mechanisms that produce allocations with fairness guarantees. However, in the standard setting without monetary transfers, it is generally impossible to have truthful mechanisms that provide non-trivial fairness guarantees. Recently, Amanatidis et al. [2021] suggested the study of mechanisms that produce fair allocations in their equilibria. Specifically, when the agents have additive valuation functions, the simple Round-Robin algorithm always has pure Nash equilibria and the corresponding allocations are envy-free up to one good (EF1) with respect to the agents' true valuation functions. Following this agenda, we show that this outstanding property of the Round-Robin mechanism extends much beyond the above default assumption of additivity. In particular, we prove that for agents with cancelable valuation functions (a natural class that contains, e.g., additive and budget-additive functions), this simple mechanism always has equilibria and even its approximate equilibria correspond to approximately EF1 allocations with respect to the agents' true valuation functions. Further, we show that the approximate EF1 fairness of approximate equilibria surprisingly holds for the important class of submodular valuation functions as well, even though exact equilibria fail to exist!

In this work we introduce a new class of mechanisms composed of a traditional Generalized Second Price (GSP) auction, and a fair division scheme in order to achieve some desired level of fairness between groups of Bayesian strategic advertisers. We propose two mechanisms, beta-Fair GSP and GSP-EFX, that compose GSP with, respectively, an envy-free up to one item, and an envy-free up to any item fair division scheme. The payments of GSP are adjusted in order to compensate advertisers that suffer a loss of efficiency due the fair division stage. We investigate the strategic learning implications of the deployment of sponsored search auction mechanisms that obey to such fairness criteria. We prove that, for both mechanisms, if bidders play so as to minimize their external regret they are guaranteed to reach an equilibrium with good social welfare. We also prove that the mechanisms are budget balanced, so that the payments charged by the traditional GSP mechanism are a good proxy of the total compensation offered to the advertisers. Finally, we evaluate the quality of the allocations through experiments on real-world data.

According to recent research, geometric deep learning allows to reach unprecedented accuracy for online misinformation detection. By fully leveraging the news social context, URL propagation paths in social networks are first represented as graphs and then classified using Graph Neural Network (GNN) models. Despite these remarkable efforts, researchers are still hampered by the scarcity of high-quality benchmark datasets, and as a result, the efficacy of state-of-the-art approaches could be overestimated. So far, in order to obtain a decent number of third-party fact-checked URLs, researchers have either sampled news from notoriously reliable and unreliable sources using distant supervision, or they have gathered pre-labeled URLs from third-party fact-checking websites. In the former case, resulting datasets can be quite large, but also noisy and biased since pieces of news are labeled as true or false according to their source label, and not individually fact-checked. In the latter case, assigned labels are more reliable, but the included news articles are usually in a single language and they may reflect unknown editorial decisions. As a result, datasets of the latter type are typically small, homogeneous, and thus unrealistically easy for automatic fake news detection models. In this work, we present FbMultiLingMisinfo, a new multilingual benchmark dataset, aimed at a more realistic evaluation of state-of-the-art misinformation detection models. URLs in our dataset come from the Facebook Privacy-Protected Full URLs Data Set, which we augmented with their propagation paths on Twitter. Our experimental results show that, when GNN-based models are tested on FbMultiLingMisinfo, recent misinformation detection results are only partially confirmed. We further show that a sharp reduction in the training size significantly reduces the model accuracy on FbMultiLingMisinfo, but not on two other widely used benchmark datasets for fake news detection.

We consider the classic online problem of scheduling on a single machine to minimize total flow time. In STOC 2021, the concept of robustness to distortion in processing times was introduced: for every distortion factor μ, an O(μ2)-competitive algorithm ALGμ which handles distortions up to μ was presented. However, using that result requires one to know the distortion of the input in advance, which is impractical. We present the first distortion-oblivious algorithms: algorithms which are competitive for every input of every distortion, and thus do not require knowledge of the distortion in advance. Moreover, the competitive ratios of our algorithms are Õ(μ), which is a quadratic improvement over the algorithm from STOC 2021, and is nearly optimal (we show a randomized lower bound of Ω(μ) on competitiveness).

We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available. Besides a direct, and optimal, SSPI for the basic single choice problem [Rubinstein et al., 2020], most existing SSPI results were obtained via an elegant, but inherently lossy reduction to order-oblivious secretary (OOS) policies [Azar et al., 2014]. Motivated by this discrepancy, we develop an intuitive and versatile greedy-based technique that yields SSPIs directly rather than through the reduction to OOSs. Our results can be seen as generalizing and unifying a number of existing results in the area of prophet and secretary problems. Our algorithms significantly improve on the competitive guarantees for a number of interesting scenarios (including general matching with edge arrivals, bipartite matching with vertex arrivals, and certain matroids), and capture new settings (such as budget additive combinatorial auctions). Complementing our algorithmic results, we also consider mechanism design variants. Finally, we analyze the power and limitations of different SSPI approaches by providing a partial converse to the reduction from SSPI to OOS given by Azar et al.

Abstract Efficient and truthful mechanisms to price resources on servers/machines have been the subject of much work in recent years due to the importance of the cloud market. This paper considers revenue maximization in the online stochastic setting with non-preemptive jobs and a unit capacity server. One agent/job arrives at every time step, with parameters drawn from the underlying distribution. We design a posted-price mechanism which can be efficiently computed and is revenue-optimal in expectation and in retrospect, up to additive error. The prices are posted prior to learning the agent’s type, and the computed pricing scheme is deterministic, depending only on the length of the allotted time interval and on the earliest time the server is available. We also prove that the proposed pricing strategy is robust to imprecise knowledge of the job distribution and that a distribution learned from polynomially many samples is sufficient to obtain a near-optimal truthful pricing strategy.

Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern-day applications can render existing algorithms prohibitively slow. Moreover, frequently those instances are also inherently stochastic. Focusing on these challenges, we revisit the classic problem of maximizing a (possibly non-monotone) submodular function subject to a knapsack constraint. We present a simple randomized greedy algorithm that achieves a 5.83-approximation and runs in O(n log n) time, i.e., at least a factor n faster than other state-of-the-art algorithms. The versatility of our approach allows us to further transfer it to a stochastic version of the problem. There, we obtain a (9 + ε)-approximation to the best adaptive policy, which is the first constant approximation for non-monotone objectives. Experimental evaluation of our algorithms showcases their improved performance on real and synthetic data.

The growing need to deal with massive instances motivates the design of algorithms balancing the quality of the solution with applicability. For the latter, an important measure is the \emph{adaptive complexity}, capturing the number of sequential rounds of parallel computation needed. In this work we obtain the first \emph{constant factor} approximation algorithm for non-monotone submodular maximization subject to a knapsack constraint with \emph{near-optimal} $O(\log n)$ adaptive complexity. Low adaptivity by itself, however, is not enough: one needs to account for the total number of function evaluations (or value queries) as well. Our algorithm asks $\tilde{O}(n^2)$ value queries, but can be modified to run with only $\tilde{O}(n)$ instead, while retaining a low adaptive complexity of $O(\log^2n)$. Besides the above improvement in adaptivity, this is also the first \emph{combinatorial} approach with sublinear adaptive complexity for the problem and yields algorithms comparable to the state-of-the-art even for the special cases of cardinality constraints or monotone objectives. Finally, we showcase our algorithms’ applicability on real-world datasets.

Bilateral trade, a fundamental topic in economics, models the problem of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. Despite the simplicity of this problem, a classical result by Myerson and Satterthwaite (1983) affirms the impossibility of designing a mechanism that is simultaneously efficient, incentive compatible, individually rational, and budget balanced. This impossibility result fostered an intense investigation of meaningful trade-offs between these desired properties. Much work has focused on approximately efficient fixed-price mechanisms, e.g., Blumrosen and Dobzinski (2014, 2016), Colini-Baldeschi et al. (2016), which have been shown to fully characterize strong budget balanced and ex-post individually rational direct revelation mechanisms. All these results, however, either assume some knowledge on the priors of the seller/buyer valuations, or black-box access to some samples of the distributions, as in Dütting et al. (2021). In this paper, we cast for the first time the bilateral trade problem in a regret minimization framework over T rounds of seller/buyer interactions, with no prior knowledge on their private valuations. Our main contribution is a complete characterization of the regret regimes for fixed-price mechanisms with different feedback models and private valuations, using as a benchmark the best fixed-price in hindsight. More precisely, we prove the following bounds on the regret ~Θ (√T) for full-feedback (i.e., direct revelation mechanisms); ~Θ(T2/3) for realistic feedback (i.e., posted-price mechanisms) and independent seller/buyer valuations with bounded densities; Θ(T) for realistic feedback and seller/buyer valuations with bounded densities; Θ(T) for realistic feedback and independent seller/buyer valuations; Θ(T) for the adversarial setting.

We consider the problem of online scheduling on a single machine in order to minimize weighted flow time. The existing algorithms for this problem (STOC ’01, SODA ’03, FOCS ’18) all require exact knowledge of the processing time of each job. This assumption is crucial, as even a slight perturbation of the processing time would lead to polynomial competitive ratio. However, this assumption very rarely holds in real-life scenarios.

A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to relax welfare efficiency and the use of approximation mechanisms. Such mechanisms in general make extensive use of the Bayesian priors. In this work, we investigate a question of increasing theoretical and practical importance: how much prior information is required to design mechanisms with near-optimal approximations? Our first contribution is a more general impossibility result stating that no meaningful approximation is possible without any prior information, expanding the famous impossibility result of Myerson and Satterthwaite. Our second contribution is that one single sample (one number per item), arguably a minimum-possible amount of prior information, from each seller distribution is sufficient for a large class of two-sided markets. We prove matching upper and lower bounds on the best approximation that can be obtained with one single sample for subadditive buyers and additive sellers, regardless of computational considerations. Our third contribution is the design of computationally efficient blackbox reductions that turn any one-sided mechanism into a two-sided mechanism with a small loss in the approximation, while using only one single sample from each seller. On the way, our blackbox-type mechanisms deliver several interesting positive results in their own right, often beating even the state of the art that uses full prior information.

We study the problem of an online advertising system that wants to optimally spend an advertiser’s given budget for a campaign across multiple platforms, without knowing the value for showing an ad to the users on those platforms. We model this challenging practical application as a Stochastic Bandits with Knapsacks problem over T rounds of bidding with the set of arms given by the set of distinct bidding m-tuples, where m is the number of platforms. We modify the algorithm proposed in Badanidiyuru et al., [11] to extend it to the case of multiple platforms to obtain an algorithm for both the discrete and continuous bid-spaces. Namely, for discrete bid spaces we give an algorithm with regret , where OPT is the performance of the optimal algorithm that knows the distributions. For continuous bid spaces the regret of our algorithm is . When restricted to this special-case, this bound improves over Sankararaman and Slivkins [34] in the regime OPT < < T, as is the case in the particular application at hand. Second, we show an lower bound for the discrete case and an Ω(m1/3B2/3) lower bound for the continuous setting, almost matching the upper bounds. Finally, we use a real-world data set from a large internet online advertising company with multiple ad platforms and show that our algorithms outperform common benchmarks and satisfy the required properties warranted in the real-world application.

Abstract Motivated by many practical applications, in this paper we study budget feasible mechanisms with the goal of procuring an independent set of a matroid. More specifically, we are given a matroid $${\mathcal {M}}=(E,{\mathcal {I}})$$ M = ( E , I ) . Each element of the ground set E is controlled by a selfish agent and the cost of the element is private information of the agent itself. A budget limited buyer has additive valuations over the elements of E. The goal is to design an incentive compatible budget feasible mechanism which procures an independent set of the matroid of largest possible value. We also consider the more general case of the pair $${\mathcal {M}}=(E,{\mathcal {I}})$$ M = ( E , I ) satisfying only the hereditary property. This includes matroids as well as matroid intersection. We show that, given a polynomial time deterministic algorithm that returns an $$\alpha $$ α -approximation to the problem of finding a maximum-value independent set in $${\mathcal {M}}$$ M , there exists an individually rational, truthful and budget feasible mechanism which is $$(3\alpha +1)$$ ( 3 α + 1 ) -approximated and runs in polynomial time, thus yielding also a 4-approximation for the special case of matroids.

Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern-day applications can render existing algorithms prohibitively slow. Moreover, frequently those instances are also inherently stochastic. Focusing on these challenges, we revisit the classic problem of maximizing a (possibly non-monotone) submodular function subject to a knapsack constraint. We present a simple randomized greedy algorithm that achieves a $5.83$ approximation and runs in $O(n \log n)$ time, i.e., at least a factor $n$ faster than other state-of-the-art algorithms. The robustness of our approach allows us to further transfer it to a stochastic version of the problem. There, we obtain a 9-approximation to the best adaptive policy, which is the first constant approximation for non-monotone objectives. Experimental evaluation of our algorithms showcases their improved performance on real and synthetic data.

The Pandora's Box Problem, originally formalized by Weitzman in 1979, models selection from a set of options each with stochastic parameters, when evaluation (i.e. sampling) is costly. This includes, for example, the problem of hiring a skilled worker, where only one hire can be made, but the evaluation of each candidate is an expensive procedure.

Incentive compatibility (IC) is a desirable property for any auction mechanism, including those used in online advertising. However, in real world applications practical constraints and complex environments often result in mechanisms that lack incentive compatibility. Recently, several papers investigated the problem of deploying black-box statistical tests to determine if an auction mechanism is incentive compatible by using the notion of IC-Regret that measures the regret of a truthful bidder. Unfortunately, most of those methods are computationally intensive, since they require the execution of many counterfactual experiments.

Exploring large-scale networks is a time consuming and expensive task which is usually operated in a complex and uncertain environment. A crucial aspect of network exploration is the development of suitable strategies that decide which nodes and edges to probe at each stage of the process. To model this process, we introduce the stochastic graph exploration problem. The input is an undirected graph G=(V,E) with a source vertex s, stochastic edge costs drawn from a distribution pi_e, e in E, and rewards on vertices of maximum value R. The goal is to find a set F of edges of total cost at most B such that the subgraph of G induced by F is connected, contains s, and maximizes the total reward. This problem generalizes the stochastic knapsack problem and other stochastic probing problems recently studied. Our focus is on the development of efficient nonadaptive strategies that are competitive against the optimal adaptive strategy. A major challenge is the fact that the problem has an Omega(n) adaptivity gap even on a tree of n vertices. This is in sharp contrast with O(1) adaptivity gap of the stochastic knapsack problem, which is a special case of our problem. We circumvent this negative result by showing that O(log nR) resource augmentation suffices to obtain O(1) approximation on trees and O(log nR) approximation on general graphs. To achieve this result, we reduce stochastic graph exploration to a memoryless process - the minesweeper problem - which assigns to every edge a probability that the process terminates when the edge is probed. For this problem, interesting in its own, we present an optimal polynomial time algorithm on trees and an O(log nR) approximation for general graphs. We study also the problem in which the maximum cost of an edge is a logarithmic fraction of the budget. We show that under this condition, there exist polynomial-time oblivious strategies that use 1+epsilon budget, whose adaptivity gaps on trees and general graphs are 1+epsilon and 8+epsilon, respectively. Finally, we provide additional results on the structure and the complexity of nonadaptive and adaptive strategies.

We study the matching problem in the incremental setting, where we are given a sequence of edge insertions and aim at maintaining a near-maximum cardinality matching of the graph with small update time. We present a deterministic algorithm that, for any constant ε > 0, maintains a (1 + ε)-approximate matching with constant amortized update time per insertion.

We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem , under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE). We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players.

Although freelancing work has grown substantially in recent years, in part facilitated by a number of online labor marketplaces, %(e.g., Guru, Freelancer, Amazon Mechanical Turk), traditional forms of "in-sourcing" work continue being the dominant form of employment. % in most companies. This means that, at least for the time being, freelancing and salaried employment will continue to co-exist. In this paper, we provide algorithms for outsourcing and hiring workers in a general setting, where workers form a team and contribute different skills to perform a task. We call this model team formation with outsourcing. In our model, tasks arrive in an online fashion: neither the number nor the composition of the tasks are known a-priori. At any point in time, there is a team of hired workers who receive a fixed salary independently of the work they perform. This team is dynamic: new members can be hired and existing members can be fired, at some cost. Additionally, some parts of the arriving tasks can be outsourced and thus completed by non-team members, at a premium. Our contribution is an efficient online cost-minimizing algorithm for hiring and firing team members and outsourcing tasks. We present theoretical bounds obtained using a primal--dual scheme proving that our algorithms have logarithmic competitive approximation ratio. We complement these results with experiments using semi-synthetic datasets based on actual task requirements and worker skills from three large online labor marketplaces.

We study the problem of unsplittable flow on a path (UFP), which arises naturally in many applications such as bandwidth allocation, job scheduling, and caching. Here we are given a path with nonnegative edge capacities and a set of tasks, which are characterized by a subpath, a demand, and a profit. The goal is to find the most profitable subset of tasks whose total demand does not violate the edge capacities. Not surprisingly, this problem has received a lot of attention in the research community. If the demand of each task is at most a small-enough fraction δ of the capacity along its subpath (δ- small tasks ), then it has been known for a long time [Chekuri et al., ICALP 2003] how to compute a solution of value arbitrarily close to the optimum via LP rounding. However, much remains unknown for the complementary case, that is, when the demand of each task is at least some fraction δ > 0 of the smallest capacity of its subpath (δ- large tasks ). For this setting, a constant factor approximation is known, improving on an earlier logarithmic approximation [Bonsma et al., FOCS 2011]. In this article, we present a polynomial-time approximation scheme (PTAS) for δ-large tasks, for any constant δ > 0. Key to this result is a complex geometrically inspired dynamic program. Each task is represented as a segment underneath the capacity curve, and we identify a proper maze-like structure so that each corridor of the maze is crossed by only O (1) tasks in the optimal solution. The maze has a tree topology, which guides our dynamic program. Our result implies a 2+ε approximation for UFP, for any constant ε > 0, improving on the previously best 7+ε approximation by Bonsma et al. We remark that our improved approximation algorithm matches the best known approximation ratio for the considerably easier special case of uniform edge capacities.

Consider the following variant of the set cover problem. We are given a universe U={1,...,n} and a collection of subsets C = {S_1,...,S_m} where each S_i is a subset of U. For every element u from U we need to find a set phi(u) from collection C such that u belongs to phi(u). Once we construct and fix the mapping phi from U to C a subset X from the universe U is revealed, and we need to cover all elements from X with exactly phi(X), that is {phi(u)}_{all u from X}. The goal is to find a mapping such that the cover phi(X) is as cheap as possible. This is an example of a universal problem where the solution has to be created before the actual instance to deal with is revealed. Such problems appear naturally in some settings when we need to optimize under uncertainty and it may be actually too expensive to begin finding a good solution once the input starts being revealed. A rich body of work was devoted to investigate such problems under the regime of worst case analysis, i.e., when we measure how good the solution is by looking at the worst-case ratio: universal solution for a given instance vs optimum solution for the same instance. As the universal solution is significantly more constrained, it is typical that such a worst-case ratio is actually quite big. One way to give a viewpoint on the problem that would be less vulnerable to such extreme worst-cases is to assume that the instance, for which we will have to create a solution, will be drawn randomly from some probability distribution. In this case one wants to minimize the expected value of the ratio: universal solution vs optimum solution. Here the bounds obtained are indeed smaller than when we compare to the worst-case ratio. But even in this case we still compare apples to oranges as no universal solution is able to construct the optimum solution for every possible instance. What if we would compare our approximate universal solution against an optimal universal solution that obeys the same rules as we do? We show that under this viewpoint, but still in the stochastic variant, we can indeed obtain better bounds than in the expected ratio model. For example, for the set cover problem we obtain $H_n$ approximation which matches the approximation ratio from the classic deterministic setup. Moreover, we show this for all possible probability distributions over $U$ that have a polynomially large carrier, while all previous results pertained to a model in which elements were sampled independently. Our result is based on rounding a proper configuration IP that captures the optimal universal solution, and using tools from submodular optimization. The same basic approach leads to improved approximation algorithms for other related problems, including Vertex Cover, Edge Cover, Directed Steiner Tree, Multicut, and Facility Location.

We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases and sales of the items. A mechanism is given prior distributions on the agents' valuations of the items, but not the actual valuations; thus the aim is to maximise the expected social welfare over these distributions. As in previous work, we are interested in the worst-case ratio between the social welfare achieved by a truthful mechanism, and the best social welfare possible.

Internet display advertising industry follows two main business models. One model is based on direct deals between publishers and advertisers where they sign legal contracts containing terms of fulfillment for a future inventory. The second model is a spot market based on auctioning page views in real-time on advertising exchange (AdX) platforms such as DoubleClick's Ad Exchange, RightMedia, or AppNexus. These exchanges play the role of intermediaries who sell items (e.g. page-views) on behalf of a seller (e.g. a publisher) to buyers (e.g., advertisers) on the opposite side of the market. The computational and economics issues arising in this second model have been extensively investigated in recent times. In this work, we consider a third emerging model called reservation exchange market. A reservation exchange is a two-sided market between buyer orders for blocks of advertisers' impressions and seller orders for blocks of publishers' page views. The goal is to match seller orders to buyer orders while providing the right incentives to both sides. In this work we first describe the important features of mechanisms for efficient reservation exchange markets. We then address the algorithmic problems of designing revenue sharing schemes to provide a fair division between sellers of the revenue collected from buyers. A major conceptual contribution of this work is in showing that even though both clinching ascending auctions and VCG mechanisms achieve the same outcome from a buyer perspective, however, from the perspective of revenue sharing among sellers, clinching ascending auctions are much more informative than VCG auctions.

Clustering is a fundamental step in many information-retrieval and data-mining applications. Detecting clusters in graphs is also a key tool for finding the community structure in social and behavioral networks. In many of these applications, the input graph evolves over time in a continual and decentralized manner, and, to maintain a good clustering, the clustering algorithm needs to repeatedly probe the graph. Furthermore, there are often limitations on the frequency of such probes, either imposed explicitly by the online platform (e.g., in the case of crawling proprietary social networks like twitter) or implicitly because of resource limitations (e.g., in the case of crawling the web). In this paper, we study a model of clustering on evolving graphs that captures this aspect of the problem. Our model is based on the classical stochastic block model, which has been used to assess rigorously the quality of various static clustering methods. In our model, the algorithm is supposed to reconstruct the planted clustering, given the ability to query for small pieces of local information about the graph, at a limited rate. We design and analyze clustering algorithms that work in this model, and show asymptotically tight upper and lower bounds on their accuracy. Finally, we perform simulations, which demonstrate that our main asymptotic results hold true also in practice.

We extend the notion of Combinatorial Walrasian Equilibrium, as defined by \citet{FGL13}, to settings with budgets. When agents have budgets, the maximum social welfare as traditionally defined is not a suitable benchmark since it is overly optimistic. This motivated the liquid welfare of \cite{DP14} as an alternative. Observing that no combinatorial Walrasian equilibrium guarantees a non-zero fraction of the maximum liquid welfare in the absence of randomization, we instead work with randomized allocations and extend the notions of liquid welfare and Combinatorial Walrasian Equilibrium accordingly. Our generalization of the Combinatorial Walrasian Equilibrium prices lotteries over bundles of items rather than bundles, and we term it a lottery pricing equilibrium.

With the rapid proliferation of microblogging services such as Twitter, a large number of tweets is published everyday often making users feel overwhelmed with information. Helping these users to discover potentially interesting tweets is an important task for such services. In this paper, we present a novel tweet-recommendation approach, which exploits network, content, and retweet analyses for making recommendations of tweets. The idea is to recommend tweets that are not visible to the user (i.e., they do not appear in the user timeline) because nobody in her social circles published or retweeted them. To do that, we create the user's ego-network up to depth two and apply the transitivity property of the friends-of-friends relationship to determine interesting recommendations, which are then ranked to best match the user's interests. Experimental results demonstrate that our approach improves the state-of-the-art technique.

Mechanism design for one-sided markets is an area of extensive research in economics and, since more than a decade, in computer science as well. Two-sided markets, on the other hand, have not received the same attention despite the numerous applications to web advertisement, stock exchange, and frequency spectrum allocation. This work studies double auctions, in which unit-demand buyers and unit-supply sellers act strategically. An ideal goal in double auction design is to maximize the social welfare of buyers and sellers with individually rational (IR), incentive compatible (IC) and strongly budget-balanced (SBB) mechanisms. The first two properties are standard. SBB requires that the payments charged to the buyers are entirely handed to the sellers. This property is crucial in all the contexts that do not allow the auctioneer retaining a share of buyers' payments or subsidizing the market. Unfortunately, this goal is known to be unachievable even for the special case of bilateral trade, where there is only one buyer and one seller. Therefore, in subsequent papers, meaningful trade-offs between these requirements have been investigated. Our main contribution is the first IR, IC and SBB mechanism that provides an O(1)-approximation to the optimal social welfare. This result holds for any number of buyers and sellers with arbitrary, independent distributions. Moreover, our result continues to hold when there is an additional matroid constraint on the sets of buyers who may get allocated an item. To prove our main result, we devise an extension of sequential posted price mechanisms to two-sided markets. In addition to this, we improve the best-known approximation bounds for the bilateral trade problem.

One of the most popular and widely used methods for data clustering is hierarchical clustering. This clustering technique has proved useful to reveal interesting structure in the data in several applications ranging from computational biology to computer vision. Robustness is an important feature of a clustering technique if we require the clustering to be stable against small perturbations in the input data. In most applications, getting a clustering output that is robust against adversarial outliers or stochastic noise is a necessary condition for the applicability and effectiveness of the clustering technique. This is even more critical in hierarchical clustering where a small change at the bottom of the hierarchy may propagate all the way through to the top. Despite all the previous work, our theoretical understanding of robust hierarchical clustering is still limited and several hierarchical clustering algorithms are not known to satisfy such robustness properties. In this paper, we study the limits of robust hierarchical $k$-center clustering by introducing the concept of universal hierarchical clustering and provide (almost) tight lower and upper bounds for the robust hierarchical $k$-center clustering problem with outliers and variants of the stochastic clustering problem. Most importantly we present a constant-factor approximation for optimal hierarchical k-center with at most $z$ outliers using a universal set of at most O(z2) set of outliers and show that this result is tight. Moreover we show the necessity of using a universal set of outliers in order to compute an approximately optimal hierarchical $k$-center with a different set of outliers for each $k$.

We study the revenue performance of sequential posted price mechanisms and some natural extensions, for a general setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted price mechanisms are conceptually simple mechanisms that work by proposing a “take-it-or-leave-it” offer to each buyer. We apply sequential posted price mechanisms to single-parameter multi-unit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers. For standard sequential posted price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the case of a continuous valuation distribution when various standard assumptions hold simultaneously. In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted price mechanism is proportional to the ratio of the highest and lowest possible valuation. We prove that for two simple generalizations of these mechanisms, a better revenue performance can be achieved: if the sequential posted price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a $$\varOmega (1/\max \{1,d\})$$ fraction of the optimal revenue can be extracted, where d denotes the “degree of dependence” of the valuations, ranging from complete independence ( $$d=0$$ ) to arbitrary dependence ( $$d = n-1$$ ). When we generalize the sequential posted price mechanisms further, such that the mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer that depends on the valuations of all buyers except i, we prove that a constant fraction $$(2 - \sqrt{e})/4 \approx 0.088$$ of the optimal revenue can be always extracted.

We design algorithms that, given a collection of documents and a distribution over user queries, return a small subset of the document collection in such a way that we can efficiently provide high-quality answers to user queries using only the selected subset. This approach has applications when space is a constraint or when the query-processing time increases significantly with the size of the collection. We study our algorithms through the lens of stochastic analysis and prove that even though they use only a small fraction of the entire collection, they can provide answers to most user queries, achieving a performance close to the optimal. To complement our theoretical findings, we experimentally show the versatility of our approach by considering two important cases in the context of Web search. In the first case, we favor the retrieval of documents that are relevant to the query, whereas in the second case we aim for document diversification. Both the theoretical and the experimental analysis provide strong evidence of the potential value of query covering in diverse application scenarios.

We study the unsplittable flow on a path problem (UFP), which arises naturally in many applications such as bandwidth allocation, job scheduling, and caching. Here we are given a path with nonnegative edge capacities and a set of tasks, which are characterized by a subpath, a demand, and a profit. The goal is to find the most profitable subset of tasks whose total demand does not violate the edge capacities. Not surprisingly this problem has received a lot of attention in the research community. If the demand of each task is at most a small enough fraction δ of the capacity along its subpath (δ-small tasks), then it has been known for a long time [Chekuri et al., ICALP 2003] how to compute a solution of value arbitrarily close to the optimum via LP rounding. However, much remains unknown for the complementary case, that is, when the demand of each task is at least some fraction δ > 0 of the smallest capacity of its subpath (δ-large tasks). For this setting a constant factor approximation, improving on an earlier logarithmic approximation, was found only recently [Bonsma et al., FOCS 2011]. In this paper we present a PTAS for δ-large tasks, for any constant δ > 0. Key to this result is a complex geometrically inspired dynamic program. Each task is represented as a segment underneath the capacity curve, and we identify a proper maze-like structure so that each corridor of the maze is crossed by only O(1) tasks in the optimal solution. The maze has a tree topology, which guides our dynamic program. Our result implies a 2 + ∊ approximation for UFP, for any constant ∊ > 0, improving on the previously best 7 + ∊ approximation by Bonsma et al. We remark that our improved approximation algorithm matches the best known approximation ratio for the considerably easier special case of uniform edge capacities.

We study the problem of computing similarity rankings in large-scale multi-categorical bipartite graphs, where the two sides of the graph represent actors and items, and the items are partitioned into an arbitrary set of categories. The problem has several real-world applications, including identifying competing advertisers and suggesting related queries in an online advertising system or finding users with similar interests and suggesting content to them. In these settings, we are interested in computing on-the-fly rankings of similar actors, given an actor and an arbitrary subset of categories of interest. Two main challenges arise: First, the bipartite graphs are huge and often lopsided (e.g. the system might receive billions of queries while presenting only millions of advertisers). Second, the sheer number of possible combinations of categories prevents the pre-computation of the results for all of them. We present a novel algorithmic framework that addresses both issues for the computation of several graph-theoretical similarity measures, including # common neighbors, and Personalized PageRank. We show how to tackle the imbalance in the graphs to speed up the computation and provide efficient real-time algorithms for computing rankings for an arbitrary subset of categories. Finally, we show experimentally the accuracy of our approach with real-world data, using both public graphs and a very large dataset from Google AdWords.

In a classic optimization problem, the complete input data is assumed to be known to the algorithm. This assumption may not be true anymore in optimization problems motivated by the Internet where part of the input data is private knowledge of independent selfish agents. The goal of algorithmic mechanism design is to provide (in polynomial time) a solution to the optimization problem and a set of incentives for the agents such that disclosing the input data is a dominant strategy for the agents. In the case of NP-hard problems, the solution computed should also be a good approximation of the optimum. In this paper we focus on mechanism design for multiobjective optimization problems. In this setting we are given a main objective function and a set of secondary objectives which are modeled via budget constraints. Multiobjective optimization is a natural setting for mechanism design as many economical choices ask for a compromise between different, partially conflicting goals. The main contribution of this paper is showing that two of the main tools for the design of approximation algorithms for multiobjective optimization problems, namely, approximate Pareto sets and Lagrangian relaxation, can lead to truthful approximation schemes. By exploiting the method of approximate Pareto sets, we devise truthful deterministic and randomized multicriteria fully polynomial-time approximation schemes (FPTASs) for multiobjective optimization problems whose exact version admits a pseudopolynomial-time algorithm, as, for instance, the multibudgeted versions of minimum spanning tree, shortest path, maximum (perfect) matching, and matroid intersection. Our construction also applies to multidimensional knapsack and multiunit combinatorial auctions. Our FPTASs compute a $(1+\varepsilon)$-approximate solution violating each budget constraint by a factor $(1+\varepsilon)$. When feasible solutions induce an independence system, i.e., when subsets of feasible solutions are feasible as well, we present a PTAS (not violating any constraint), which combines the approach above with a novel monotone way to guess the heaviest elements in the optimum solution. Finally, we present a universally truthful Las Vegas PTAS for minimum spanning tree with a single budget constraint, where one wants to compute a minimum cost spanning tree whose length is at most a given value $L$. This result is based on the Lagrangian relaxation method, in combination with our monotone guessing step and with a random perturbation step (ensuring low expected running time). This result can be derandomized in the case of integral lengths. All the mentioned results match the best known approximation ratios, which are, however, obtained by nontruthful algorithms.

We construct prior-free auctions with constant-factor approximation guarantees with ordered bidders, in both unlimited and limited supply settings. We compare the expected revenue of our auctions on a bid vector to the monotone price benchmark, the maximum revenue that can be obtained from a bid vector using supply-respecting prices that are nonincreasing in the bidder ordering and bounded above by the second-highest bid. As a consequence, our auctions are simultaneously near-optimal in a wide range of Bayesian multi-unit environments.

Given a universe $U$ of $n$ elements and a weighted collection $\mathscr{S}$ of $m$ subsets of $U$, the universal set cover problem is to a priori map each element $u \in U$ to a set $S(u) \in \mathscr{S}$ containing $u$ such that any set $X{\subseteq U}$ is covered by $S(X)=\cup_{u\in XS(u)$. The aim is to find a mapping such that the cost of $S(X)$ is as close as possible to the optimal set cover cost for $X$. (Such problems are also called oblivious or a priori optimization problems.) Unfortunately, for every universal mapping, the cost of $S(X)$ can be $\Omega(\sqrt{n})$ times larger than optimal if the set $X$ is adversarially chosen. In this paper we study the performance on average, when $X$ is a set of randomly chosen elements from the universe: we show how to efficiently find a universal map whose expected cost is $O(\log mn)$ times the expected optimal cost. In fact, we give a slightly improved analysis and show that this is the best possible. We generalize these ideas to weighted set cover and show similar guarantees to (nonmetric) facility location, where we have to balance the facility opening cost with the cost of connecting clients to the facilities. We show applications of our results to universal multicut and disc-covering problems and show how all these universal mappings give us algorithms for the stochastic online variants of the problems with the same competitive factors.

We study envy-free (EF) mechanisms for multi-unit auctions with budgeted agents that approximately maximize revenue. In an EF auction, prices are set so that every bidder receives a bundle that maximizes her utility amongst all bundles; We show that the problem of revenue-maximizing EF auctions is NP-hard, even for the case of identical items and additive valuations (up to the budget). The main result of our paper is a novel EF auction that runs in polynomial time and provides a approximation of 1/2 with respect to the revenue-maximizing EF auction. A slight variant of our mechanism will produce an allocation and pricing that is more restrictive (so called item pricing) and gives a 1/2 approximation to the optimal revenue within this more restrictive class.

Prior-free auctions are robust auctions that assume no distribution over bidders' valuations and provide worst-case (input-by-input) approximation guarantees. In contrast to previous work on this topic, we pursue good prior-free auctions with non-identical bidders.

We study the problem of online team formation. We consider a setting in which people possess different skills and compatibility among potential team members is modeled by a social network. A sequence of tasks arrives in an online fashion, and each task requires a specific set of skills. The goal is to form a new team upon arrival of each task, so that (i) each team possesses all skills required by the task, (ii) each team has small communication overhead, and (iii) the workload of performing the tasks is balanced among people in the fairest possible way.

In a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least k nodes of an edge-weighted graph. Here, nodes represent requests whereas edges correspond to items. In this paper, we initiate the study of a new family of multi-layer covering problems. Each such problem consists of a collection of h distinct instances of a standard covering problem (layers), with the constraint that all layers share the same set of requests. We identify two main subfamilies of these problems: - in an union multi-layer problem, a request is satisfied if it is satisfied in at least one layer; - in an intersection multi-layer problem, a request is satisfied if it is satisfied in all layers. To see some natural applications, consider both generalizations of k-MST. Union k-MST can model a problem where we are asked to connect a set of users to at least one of two communication networks, e.g., a wireless and a wired network. On the other hand, Intersection k-MST can formalize the problem of providing both electricity and water to at least k users.

We consider budget constrained combinatorial auctions where each bidder has a private value for each of the items in some subset of the items and an overall budget constraint. Such auctions capture adword auctions, where advertisers offer a bid for those adwords that (hopefully) target their intended audience, and advertisers also have budgets. It is known that even if all items are identical and all budgets are public it is not possible to be truthful and efficient. Our main result is a novel auction that runs in polynomial time, is incentive compatible, and ensures Pareto-optimality. The auction is incentive compatible with respect to the private valuations whereas the budgets and the sets of interest are assumed to be public knowledge. This extends the result of Dobzinski, Lavi and Nisan (FOCS 2008) for auctions of multiple identical items with bugets to single-valued combinatorial auctions and address one of the basic challenges on auctioning web ads (see Nisan et al, 2009, Google auctions for tv ads).

In this paper we introduce the problem of query covering as a means to efficiently cache query results. The general idea is to populate the cache with documents that contribute to the result pages of a large number of queries, as opposed to caching the top documents for each query. It turns out that the problem is hard and solving it requires knowledge of the structure of the queries and the results space, as well as knowledge of the input query distribution. We formulate the problem under the framework of stochastic optimization; theoretically it can be seen as a stochastic universal version of set multicover. While the problem is NP-hard to be solved exactly, we show that for any distribution it can be approximated using a simple greedy approach. Our theoretical findings are complemented by experimental activity on real datasets, showing the feasibility and potential interest of query-covering approaches in practice.

The internet has enabled the collaboration of groups at a scale that was unseen before. A key problem for large collaboration groups is to be able to allocate tasks effectively. An effective task assignment method should consider both how fit teams are for each job as well as how fair the assignment is to team members, in terms that no one should be overloaded or unfairly singled out. The assignment has to be done automatically or semi-automatically given that it is difficult and time-consuming to keep track of the skills and the workload of each person. Obviously the method to do this assignment must also be computationally efficient.

In a classic optimization problem the complete input data is known to the algorithm. This assumption may not be true anymore in optimization problems motivated by the Internet where part of the input data is private knowledge of independent selfish agents. The goal of algorithmic mechanism design is to provide (in polynomial time) a solution to the optimization problem and a set of incentives for the agents such that disclosing the input data is a dominant strategy for the agents. In case of NP-hard problems, the solution computed should also be a good approximation of the optimum. In this paper we focus on mechanism design for multi-objective optimization problems, where we are given the main objective function, and a set of secondary objectives which are modeled via budget constraints. Multi-objective optimization is a natural setting for mechanism design as many economical choices ask for a compromise between different, partially conflicting, goals. Our main contribution is showing that two of the main tools for the design of approximation algorithms for multi-objective optimization problems, namely approximate Pareto curves and Lagrangian relaxation, can lead to truthful approximation schemes. By exploiting the method of approximate Pareto curves, we devise truthful FPTASs for multi-objective optimization problems whose exact version admits a pseudo-polynomial-time algorithm, as for instance the multi-budgeted versions of minimum spanning tree, shortest path, maximum (perfect) matching, and matroid intersection. Our technique applies also to multi-dimensional knapsack and multi-unit combinatorial auctions. Our FPTASs compute a (1 + ε)-approximate solution violating each budget constraint by a factor (1 + ε). For a relevant sub-class of the mentioned problems we also present a PTAS (not violating any constraint), which combines the approach above with a novel monotone way to guess the heaviest elements in the optimum solution. Finally we present a universally truthful Las Vegas PTAS for minimum spanning tree with a single budget constraint. This result is based on the Lagrangian relaxation method, in combination with our monotone guessing step and a random perturbation step (ensuring low expected running time in a way similar to the smoothed analysis of algorithms). All the mentioned results match the best known approximation ratios, which however are obtained by non-truthful algorithms.

Gupta et al. [J. ACM, 54 (2007), article 11] and Gupta, Kumar, and Roughgarden [in Proceedings of the ACM Symposium on Theory of Computing, ACM, New York, 2003, pp. 365–372] recently developed an elegant framework for the development of randomized approximation algorithms for rent-or-buy network design problems. The essential building block of this framework is an approximation algorithm for the underlying network design problem that admits a strict cost sharing scheme. Such cost sharing schemes have also proven to be useful in the development of approximation algorithms in the context of two-stage stochastic optimization with recourse. The main contribution of this paper is to show that the Steiner forest problem admits cost shares that are 3-strict and 4-group-strict. As a consequence, we derive surprisingly simple approximation algorithms for the multicommodity rent-or-buy and the multicast rent-or-buy problems with approximation ratios 5 and 6, improving over the previous best approximation ratios of 6.828 and 12.8, respectively. We also show that no approximation ratio better than 4.67 can be achieved using the sample-and-augment framework in combination with the currently best known Steiner forest approximation algorithms. In the context of two-stage stochastic optimization, our result leads to a 6-approximation algorithm for the stochastic Steiner tree problem in the black-box model and a 5-approximation algorithm for the stochastic Steiner forest problem in the independent decision model.

Given a universe U of n elements and a weighted collection l of m subsets of U, the universal set cover problem is to a-priori map each element u epsi U to a set S(u) epsi l containing u, so that X sube U is covered by S(X)=UuepsiXS(u). The aim is finding a mapping such that the cost of S(X) is as close as possible to the optimal set-cover cost for X. (Such problems are also called oblivious or a-priori optimization problems.) Unfortunately, for every universal mapping, the cost of S(X) can be Omega(radicn) times larger than optimal if the set X is adversarially chosen. In this paper we study the performance on average, when X is a set of randomly chosen elements from the universe: we show how to efficiently find a universal map whose expected cost is O(log mn) times the expected optimal cost. In fact, we give a slightly improved analysis and show that this is the best possible. We generalize these ideas to weighted set cover and show similar guarantees to (non-metric) facility location, where we have to balance the facility opening cost with the cost of connecting clients to the facilities. We show applications of our results to universal multi-cut and disc-covering problems, and show how all these universal mappings give us stochastic online algorithms with the same competitive factors.

The problem of mining frequent patterns in networks has many applications, including analysis of complex networks, clustering of graphs, finding communities in social networks, and indexing of graphical and biological databases. Despite this wealth of applications, the current state of the art lacks algorithmic tools for counting the number of subgraphs contained in a large network. In this paper we develop data-stream algorithms that approximate the number of all subgraphs of three and four vertices in directed and undirected networks. We use the frequency of occurrence of all subgraphs to prove their significance in order to characterize different kinds of networks: we achieve very good precision in clustering networks with similar structure. The significance of our method is supported by the fact that such high precision cannot be achieved when performing clustering based on simpler topological properties, such as degree, assortativity, and eigenvector distributions. We have also tested our techniques using swap randomization.

We consider a game-theoretical variant of the Steiner forest problem in which each player j, out of a set of k players, strives to connect his terminal pair $(s_j, t_j)$ of vertices in an undirected, edge-weighted graph G. In this paper we show that a natural adaptation of the primal-dual Steiner forest algorithm of Agrawal, Klein, and Ravi [SIAM J. Comput., 24 (1995), pp. 445–456] yields a 2-budget balanced and cross-monotonic cost sharing method for this game. We also present a negative result, arguing that no cross-monotonic cost sharing method can achieve a budget balance factor of less than 2 for the Steiner tree game. This shows that our result is tight. Our algorithm gives rise to a new linear programming relaxation for the Steiner forest problem which we term the lifted-cut relaxation. We show that this new relaxation is stronger than the standard undirected cut relaxation for the Steiner forest problem.

We propose link-based techniques for automatic detection of Web spam, a term referring to pages which use deceptive techniques to obtain undeservedly high scores in search engines. The use of Web spam is widespread and difficult to solve, mostly due to the large size of the Web which means that, in practice, many algorithms are infeasible. We perform a statistical analysis of a large collection of Web pages. In particular, we compute statistics of the links in the vicinity of every Web page applying rank propagation and probabilistic counting over the entire Web graph in a scalable way. These statistical features are used to build Web spam classifiers which only consider the link structure of the Web, regardless of page contents. We then present a study of the performance of each of the classifiers alone, as well as their combined performance, by testing them over a large collection of Web link spam. After tenfold cross-validation, our best classifiers have a performance comparable to that of state-of-the-art spam classifiers that use content attributes, but are orthogonal to content-based methods.

The quality of Nash equilibria in network formations games has recently been analyzed in the case of uncoordinated players. In this paper we study how the price of anarchy of network formation games with Shapley cost allocation is affected by allowing locally coordinated coalitions of players. In a distributed setting not all users can communicate and form coalitions, at least they have to know that the others exist. Here, we assume that the users can form a coalition when they share a resource, i.e., in our case a group of users that share an edge can form a coalition. We show that this assumption is strong enough to decrease the price of anarchy from Θ(k) to Θ(log k) in the one terminal undirected case, where every vertex node is associated with a player and k is the number of players. Whereas in the directed or multi terminal case local communication does not necessary lead to a better price of anarchy. We additionally show that in the directed case the price of stability increases from Θ(log k) to Θ(k).

In the multicommodity rent-or-buy (MROB) network design problems, we are given a network together with a set of k terminal pairs ( s 1 , t 1 ), …, ( s k , t k . The goal is to provision the network so that a given amount of flow can be shipped between s i and t i for all 1 ≤ i ≤ k simultaneously. In order to provision the network, one can either rent capacity on edges at some cost per unit of flow, or buy them at some larger fixed cost. Bought edges have no incremental, flow-dependent cost. The overall objective is to minimize the total provisioning cost. Recently, Gupta et al. [2003a] presented a 12-approximation for the MROB problem. Their algroithm chooses a subset of the terminal pairs in the graph at random and then buys the edges of an approximate Steiner forest for these pairs. This technique had previously been introduced [Gupta et al. 2003b] for the single-sink rent-or-buy network design problem. In this article we give a 6.828-approximation for the MROB problem by refining the algorithm of Gupta et al. and simplifying their analysis. The improvement in our article is based on a more careful adaptation and simplified analysis of the primal-dual algorithm for the Steiner forest problem due to Agrawal et al. [1995]. Our result significantly reduces the gap between the single-sink and multisink case.

In this article we present an experimental study of the properties of webgraphs. We study a large crawl from 2001 of 200M pages and about 1.4 billion edges, made available by the WebBase project at Stanford, as well as several synthetic ones generated according to various models proposed recently. We investigate several topological properties of such graphs, including the number of bipartite cores and strongly connected components, the distribution of degrees and PageRank values and some correlations; we present a comparison study of the models against these measures.Our findings are that (i) the WebBase sample differs slightly from the (older) samples studied in the literature, and (ii) despite the fact that these models do not catch all of its properties, they do exhibit some peculiar behaviors not found, for example, in the models from classical random graph theory.Moreover we developed a software library able to generate and measure massive graphs in secondary memory; this library is publicy available under the GPL licence. We discuss its implementation and some computational issues related to secondary memory graph algorithms.

We present two space bounded random sampling algorithms that compute an approximation of the number of triangles in an undirected graph given as a stream of edges. Our first algorithm does not make any assumptions on the order of edges in the stream. It uses space that is inversely related to the ratio between the number of triangles and the number of triples with at least one edge in the induced subgraph, and constant expected update time per edge. Our second algorithm is designed for incidence streams (all edges incident to the same vertex appear consecutively). It uses space that is inversely related to the ratio between the number of triangles and length 2 paths in the graph and expected update time O(log |V |·(1+s ·|V |/|E|)), where s is the space requirement of the algorithm. These results significantly improve over previous work [20, 8]. Since the space complexity depends only on the structure of the input graph and not on the number of nodes, our algorithms scale very well with increasing graph size and so they provide a basic tool to analyze the structure of large graphs. They have many applications, for example, in the discovery of Web communities, the computation of clustering and transitivity coefficient, and discovery of frequent patterns in large graphs. We have implemented both algorithms and evaluated their performance on networks from different application domains. The sizes of the considered graphs varied from about 8, 000 nodes and 40, 000 edges to 135 million nodes and more than 1 billion edges. For both algorithms we run experiments with parameter s = 1, 000, 10, 000, 100, 000, 1, 000, 000 to evaluate running time and approximation guarantee. Both algorithms appear to be time efficient for these sample sizes. The approximation quality of the first algorithm was varying significantly and even for s = 1, 000, 000 we had more than 10% deviation for more than half of the instances. The second algorithm performed much better and even for s = 10, 000 we had an average deviation of less than 6% (taken over all but the largest instance for which we could not compute the number of triangles exactly). Copyright 2006 ACM.

In the multi-commodity rent-or-buy network design problem (MRoB) we are given a network together with a set of k terminal pairs R = (s_1, t_1), ..., (s_k, t_k). The goal is to install capacities on the edges of the network so that a prescribed amount of flow fi can be routed between all terminal pairs si and ti simultaneously. We can either rent capacity on an edge at some cost per unit flow or buy infinite capacity on an edge at some larger fixed cost. The overall objective is to install capacities at a minimum total cost.The version of the stochastic Steiner tree problem (SST) considered here is the Steiner tree problem in the model of two-stage stochastic optimization with recourse. In stage one, there is a known probability distribution on subsets of vertices and we can choose to buy a subset of edges at a given cost. In stage two, a subset of vertices T from the prior known distribution is realized, and additional edges can be bought at a possibly higher cost. The objective is to buy a set of edges in stages one and two so that all vertices in T are connected, and the expected cost is minimized.Gupta et al. (FOCS '03) give a randomized scheme for the MRoB problem that was both used subsequently to improve the approximation ratio for this problem, and extended to yield the best approximation algorithm for SST. One building block of this scheme is a good approximation algorithm for Steiner forests.We present a surprisingly simple 5-approximation algorithm for MRoB and 6-approximation for SST, improving on the best previous guarantees of 6.828 and 12.6, and show that no approximation ratio better than 4.67 can be achieved using the above mentioned randomized scheme in combination with the currently best known Steiner forest approximation algorithms. A key component of our approach are cost shares that are 3-strict for the unmodified primal-dual Steiner forest algorithm.

Wikipedia is an online encyclopedia, available in more than 100 languages and comprising over 1 million articles in its English version. If we consider each Wikipedia article as a node and each hyperlink between articles as an arc we have a "Wikigraph", a graph that represents the link structure of Wikipedia. The Wikigraph differs from other Web graphs studied in the literature by the fact that there are explicit timestamps associated with each node's events. This allows us to do a detailed analysis of the Wikipedia evolution over time. In the first part of this study we characterize this evolution in terms of users, editions and articles; in the second part, we depict the temporal evolution of several topological properties of the Wikigraph. The insights obtained from the Wikigraphs can be applied to large Web graphs from which the temporal data is usually not available.

We present lower bounds on the competitive ratio of randomized algorithms for a wide class of on-line graph optimization problems, and we apply such results to on-line virtual circuit and optical routing problems. Lund and Yannakakis [The approximation of maximum subgraph problems, in Proceedings of the 20th International Colloquium on Automata, Languages and Programming, 1993, pp. 40-51] give inapproximability results for the problem of finding the largest vertex induced subgraph satisfying any nontrivial, hereditary property pi--e.g., independent set, planar, acyclic, bipartite. We consider the on-line version of this family of problems, where some graph G is fixed and some subgraph H of G is presented on-line, vertex by vertex. The on-line algorithm must choose a subset of the vertices of H, choosing or rejecting a vertex when it is presented, whose vertex induced subgraph satisfies property pi. Furthermore, we study the on-line version of graph coloring whose off-line version has also been shown to be inapproximable [C. Lund and M. Yannakakis, On the hardness of approximating minimization problems, in Proceedings of the 25th ACM Symposium on Theory of Computing, 1993], on-line max edge-disjoint paths, and on-line path coloring problems. Irrespective of the time complexity, we show an Omega(n epsilon ) lower bound on the competitive ratio of randomized on-line algorithms for any of these problems. As a consequence, we obtain an Omega(n epsilon ) lower bound on the competitive ratio of randomized on-line algorithms for virtual circuit routing on general networks, in contrast to the known results for some specific networks. Similar lower bounds are obtained for on-line optical routing as well.

Abstract Next‐generation 3G/4G wireless data networks allow multiple codes (or channels) to be allocated to a single user, where each code can support multiple data rates. Providing fine‐grained QoS to users in such networks poses the two‐dimensional challenge of assigning both power (rate) and codes to every user. This gives rise to a new class of parallel scheduling problems. We abstract general downlink scheduling problems suitable for proposed next‐generation wireless data systems. Our contribution includes a communication‐theoretic model for multirate wireless channels. In addition, while conventional focus has been on throughput maximization, we attempt to optimize the maximum response time of jobs, which is more suitable for streams of user requests. We present provable results on the algorithmic complexity of these scheduling problems. In particular, we are able to provide very simple, on‐line algorithms for approximating the optimal maximum response time. We also perform an experimental study with realistic data of channel conditions and user requests that strengthens our theoretical results. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 45(1), 9–22 2005

We devise cost sharing methods for connected facility location games that are cross-monotonic, competitive and recover a constant fraction of the optimal cost.The novelty of this work is that we use randomized algorithms and that we share the expected cost among the participating users. We also provide a primal-dual cost sharing method for the connected facility location game with opening costs.

Using idle times of the processors is a well-known approach to run coarse grained parallel algorithms for extremely complex problems. We present on-line algorithms for scheduling the processes of a parallel application that is known off-line on a dynamic network in which the idle times of the processors are dictated by an adversary. We also take communication and synchronization costs into account.Our first contribution consists of a formal model to restrict the adversary in a reasonable way. We then show a constant factor approximation for the off-line scheduling problem. As this problem has to take communication cost into account, it can be seen as a generalization of many NP-hard parallel machine scheduling problems. Finally, we present on-line algorithms for different models with constant or with "nearly constant" competitive ratio.

Scheduling a sequence of jobs released over time when the processing time of a job is only known at its completion is a classical problem in CPU scheduling in time sharing operating systems. A widely used measure for the responsiveness of the system is the average flow time of the jobs, that is, the average time spent by jobs in the system between release and completion.The Windows NT and the Unix operating system scheduling policies are based on the Multilevel Feedback algorithm. In this article, we prove that a randomized version of the Multilevel Feedback algorithm is competitive for single and parallel machine systems, in our opinion providing one theoretical validation of the goodness of an idea that has proven effective in practice along the last two decades.The randomized Multilevel Feedback algorithm (RMLF) was first proposed by Kalyanasundaram and Pruhs for a single machine achieving an O (log n log log n ) competitive ratio to minimize the average flow time against the on-line adaptive adversary, where n is the number of jobs that are released. We present a version of RMLF working for any number m of parallel machines. We show for RMLF a first O (log n log n / m ) competitiveness result against the oblivious adversary on parallel machines. We also show that the same RMLF algorithm surprisingly achieves a tight O (log n ) competitive ratio against the oblivious adversary on a single machine, therefore matching the lower bound for this case.

In this paper, we introduce the notion of smoothed competitive analysis of online algorithms. Smoothed analysis has been proposed by Spielman and Teng [25] to explain the behavior of algorithms that work well in practice while performing very poorly from a worst-case analysis point of view. We apply this notion to analyze the multilevel feedback algorithm (MLF) to minimize the total flow time on a sequence of jobs released over time when the processing time of a job is only known at time of completion. The initial processing times are integers in the range [1, 2K]. We use a partial bit randomization model, i.e., the initial processing times are smoothed by changing the k least significant bits under a quite general class of probability distributions. We show that MLF admits a smoothed competitive ratio of O((2k/σ)3+ (2k/σ)22K-k), where σ denotes the standard deviation of the distribution. In particular, we obtain a competitive ratio of O(2K-k) if σ = Θ(2k). We also prove an Ω(2K-k) lower bound for any deterministic algorithm that is run on processing times smoothed according to the partial bit randomization model. For various other smoothing models, including the additive symmetric smoothing one, which is a variant of the model used by Spielman and Teng [25], we give a higher lower bound of Ω(2K). A direct consequence of our result is also the first average-case analysis of MLF. We show a constant expected ratio of the total flow time of MLF to the optimum under several distributions including the uniform one.

Next generation 3G/4G wireless data networks allow multiple codes (or channels) to be allocated to a single user, where each code can support multiple data rates. Providing fine-grained QoS to users in such networks poses the two dimensional challenge of assigning both power (rate) and codes for every user. This gives rise to a new class of parallel scheduling problems. We abstract general downlink scheduling problems suitable for proposed next generation wireless data systems. This includes a communication-theoretic model for multirate wireless channels. In addition, while conventional focus has been on throughput maximization, we attempt to optimize the maximum response time of jobs, which is more suitable for stream of user requests. We present provable results on the algorithmic complexity of these scheduling problems. In particular, we are able to provide very simple, online algorithms for approximating the optimal maximum response time. This relies on resource augmented competitive analysis. We also perform an experimental study with realistic data of channel conditions and user requests to show that our algorithms are more accurate than our worst case analysis shows, and they provide fine-grained QoS to users effectively.

We consider the classical problem of scheduling jobs in a multiprocessor setting in order to minimize the flow time (total time in the system). The performance of the algorithm, both in offline and online settings, can be significantly improved if we allow preemption, i.e., interrupt a job and later continue its execution, perhaps migrating it to a different machine. Preemption is inherent to make a scheduling algorithm efficient. While in the case of a single processor most operating systems can easily handle preemptions, migrating a job to a different machine results in a huge overhead. Thus, it is not commonly used in most multiprocessor operating systems. The natural question is whether migration is an inherent component for an efficient scheduling algorithm in either the online or offline setting. Leonardi and Raz [Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, El Paso, TX, 1997, pp. 110--119] showed that the well-known algorithm, shortest remaining processing time (SRPT), performs within a logarithmic factor of the optimal offline algorithm. Note that SRPT must use both preemption and migration to schedule the jobs. It is not known if better approximation factors can be reached and thus SRPT, although it is an online algorithm, becomes the best known algorithm in the offline setting. In fact, in the online setting, Leonardi and Raz showed that no algorithm can achieve a better bound. Without migration, no (offline or online) approximations are known. This paper introduces a new algorithm that does not use migration, works online, and is just as effective (in terms of approximation ratio) as the best known offline algorithm that uses migration.

Scheduling a sequence of jobs released over time when the processing time of a job is only known at its completion is a classical problem in CPU scheduling in time sharing operating systems. A widely used measure for the responsiveness of the system is the average flow time of the jobs, i.e. the average time spent by jobs in the system between release and completion.

We consider the problem of on-line call admission and routing on trees and meshes. Previous work gave randomized on-line algorithms for these problems and proved that they have optimal (up to constant factors) competitive ratios. However, these algorithms can obtain very low profit with high probability. We investigate the question of devising for these problems on-line competitive algorithms that also guarantee a "good" solution with "good" probability. We give a new family of randomized algorithms with asymptotically optimal competitive ratios and "good" probability to get a profit close to the expectation. We complement these results by providing bounds on the probability of any optimally competitive randomized on-line algorithm for the problems we consider to get a profit close to the expectation. To the best of our knowledge, this is the first study of the relationship between the tail distribution and the competitive ratio of randomized on-line benefit algorithms.

We consider a version ofmultiprocessor scheduling with the special feature that jobs may be rejected at a certain penalty. An instance of the problem is given by m identical parallel machines and a set of n jobs, with each job characterized by a processing time and a penalty. In the on-line version the jobs become available one by one and we have to schedule or reject a job before we have any information about future jobs. The objective is to minimize the makespan of the schedule for accepted jobs plus the sum of the penalties of rejected jobs. The main result is a $1+\phi\approx 2.618$ competitive algorithm for the on-line version of the problem, where $\phi$ is the golden ratio. A matching lower bound shows that this is the best possible algorithm working for all m. For fixed m we give improved bounds; in particular, for $m=2$ we give a $\phi\approx 1.618$ competitive algorithm, which is best possible. For the off-line problem we present a fully polynomial approximation scheme for fixed m and a polynomial approximation scheme for arbitrary m. Moreover, we present an approximation algorithm which runs in time $O(n\log n)$ for arbitrary m and guarantees a $2-\frac{1}{m}$ approximation ratio.

We consider the classical problem of scheduling jobs in a multiprocessor setting in order to minimize the flow time (tota time in the system).The performance of the algorithm, both in offline and online settings, can be significantly improved if we allow preemption: i.e., intermpt a job and later continue its execution, perhaps migrating it to a different machine.Preemption is inherent to make a scheduling algorithm efficient.While in case of a single processor, most operating systems can easily handle preemptions, migrating a job to a different machine results in a huge overhead.Thus, it is not commonly used in most multiprocessor operating systems.The natural question is whether migration is an inherent component for an efficient scheduling algorithm, in either online or offline setting.Leonardi and Raz (STOC'97) showed that the well known algorithm, shortest remaining processing time (SRF'I'), performs within a logarithmic factor of the optimal algorithm.Note that SRPT must use both preemption and migration to schedule the jobs.It is not known if better approximation factors can be reached.In fact, in the on-line setting, Leonardi and Raz showed that no algorithm

We study integrated prefetching and caching problems following the work of Cao et al. [1995] and Kimbrel and Karlin [1996]. Cao et al. and Kimbrel and Karlin gave approximation algorithms for minimizing the total elapsed time in single and parallel disk settings. The total elapsed time is the sum of the processor stall times and the length of the request sequence to be served. We show that an optimum prefetching/caching schedule for a single disk problem can be computed in polynomial time, thereby settling an open question by Kimbrel and Karlin. For the parallel disk problem, we give an approximation algorithm for minimizing stall time. The solution uses a few extra memory blocks in cache. Stall time is an important and harder to approximate measure for this problem. All of our algorithms are based on a new approach which involves formulating the prefetching/caching problems as linear programs.

Article Approximating total flow time on parallel machines Share on Authors: Stefano Leonardi Dipartimento di Informatica e Sistemistica, Università di Roma "La Sapienza" Dipartimento di Informatica e Sistemistica, Università di Roma "La Sapienza"View Profile , Danny Raz International Computer Science Institute (ICSI), Berkeley International Computer Science Institute (ICSI), BerkeleyView Profile Authors Info & Claims STOC '97: Proceedings of the twenty-ninth annual ACM symposium on Theory of computingMay 1997 Pages 110–119https://doi.org/10.1145/258533.258562Online:04 May 1997Publication History 104citation572DownloadsMetricsTotal Citations104Total Downloads572Last 12 Months8Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

In this paper we deal with the efficiency oftoken-based strategies for the basic problem of controlling the allocation of a shared resource in a ring of n processing entities. We propose new protocols that allow a bounded number of exchanged messages per access request to the resource, while this amount is unbounded for classical solutions. We also guarantee all the requests to be served within a maximum delay. The new proposed protocols are request-message-based strategies, in that a process entity sends a message to “inform” the token of the access request.

We present lower bounds on the competitive ratio of randomized algorithms for a wide class of on-line graph optimization problems and we apply such results to online virtual circuit and optical routing problems.Lund and Yannakakis [LY93a] give inapproximability results for the problem of finding the largest vertex induced subgraph satisfying any non-trivial, hereditary, property r.E.g., independent set, planar, acyclic, bipartite, etc.We consider the on-line version of this family of problems, where some graph G is fixed and some subgraph H is presented on-line, vertex by vertex.The on-line algorithm must choose a subset of the vertices of i7, choosing or rejecting a vertex when it is presented, whose vertex induced subgraph satisfies property m.Furthermore, we study the on-line version line algorithms for any of these problems.As a consequence, we obtain an fl(n') lower bound on the competitive ratio of randomized on-line algorithms for virtual circuit routing on general networks, in contrast to the known results for some specific networks.Moreover, this lower bound holds even if the use of preemption is allowed.Similar lower bounds are obtained for on-line optical routing as well,