Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems

Li, Jian; Deshpande, Amol

doi:10.1109/focs.2011.33

Cited by 18 publications

(22 citation statements)

References 46 publications

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“…We close this section with a brief discussion of some additional related literature. Li and Deshpande [12] study the problem of maximizing expected utility for various combinatorial optimization problems. They assume that the random coefficients are independent to simplify the expectation operation and use an approximation of the utility function.…”

Section: Introductionmentioning

confidence: 99%

Maximizing expected utility over a knapsack constraint

Ahmed

2016

Operations Research Letters

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The expected utility knapsack problem is to pick a set of items with random values so as to maximize the expected utility of the total value of the items picked subject to a knapsack constraint. We devise an approximation algorithm for this problem by combining sample average approximation and greedy submodular maximization. Our main result is an algorithm that maximizes an increasing submodular function over a knapsack constraint with an approximation ratio better than the well known (1-1/e) factor.

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Section: Introductionmentioning

confidence: 99%

Maximizing expected utility over a knapsack constraint

Ahmed

2016

Operations Research Letters

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“…Our solution approach for ProbFAP and HierProbFAP builds on the stochastic optimization framework of Li and Yuan (2013), which uses a Poisson approximation technique (Le Cam 1960). Other recent work on stochastic knapsack and related problems includes Bhalgat et al (2011) and Li and Deshpande (2011).…”

Section: Related Workmentioning

confidence: 99%

Robust and Probabilistic Failure-Aware Placement

Korupolu

Rajaraman

2018

ACM Trans. Parallel Comput.

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Motivated by the growing complexity and heterogeneity of modern data centers, and the prevalence of commodity component failures, this article studies the failure-aware placement problem of placing tasks of a parallel job on machines in the data center with the goal of increasing availability. We consider two models of failures: adversarial and probabilistic. In the adversarial model, each node has a weight (higher weight implying higher reliability) and the adversary can remove any subset of nodes of total weight at most a given bound W and our goal is to find a placement that incurs the least disruption against such an adversary. In the probabilistic model, each node has a probability of failure and we need to find a placement that maximizes the probability that at least K out of N tasks survive at any time. For adversarial failures, we first show that (i) the problems are in Σ 2 , the second level of the polynomial hierarchy; (ii) a variant of the problem that we call R obust F ap (for Robust Failure-Aware Placement) is co-NP-hard; and (iii) an all-or-nothing version of R obust F ap is Σ 2 -complete. We then give a polynomial-time approximation scheme (PTAS) for R obust F ap , a key ingredient of which is a solution that we design for a fractional version of R obust F ap . We then study H ier R obust F ap , which is the fractional R obust F ap problem over a hierarchical network, in which failures can occur at any subset of nodes in the hierarchy, and a failure at a node can adversely impact all of its descendants in the hierarchy. To solve H ier R obust F ap , we introduce a notion of hierarchical max-min fairness and a novel Generalized Spreading algorithm, which is simultaneously optimal for every upper bound W on the total weight of nodes that an adversary can fail. These generalize the classical notion of max-min fairness to work with nodes of differing capacities, differing reliability weights, and hierarchical structures. Using randomized rounding, we extend this to give an algorithm for integral H ier R obust F ap . For the probabilistic version, we first give an algorithm that achieves an additive ϵ approximation in the failure probability for the single level version, called P rob F ap , while giving up a (1 + ϵ) multiplicative factor in the number of failures. We then extend the result to the hierarchical version, H ier P rob F ap , achieving an ϵ additive approximation in failure probability while giving up an (L + ϵ) multiplicative factor in the number of failures, where L is the number of levels in the hierarchy.

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“…Our solution approach for ProbFAP and HierProbFAP builds on the stochastic optimization framework of Li and Yuan [24] which uses a Poisson approximation technique [22]. Other recent work on stochastic knapsack and related problems includes [5,23].…”

Section: Related Workmentioning

confidence: 99%

Robust and Probabilistic Failure-Aware Placement

Korupolu

Rajaraman

2016

Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures

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Motivated by the growing complexity and heterogeneity of modern data centers, and the prevalence of commodity component failures, this paper studies the failure-aware placement problem of placing tasks of a parallel job on machines in the data center with the goal of increasing availability. We consider two models of failures: adversarial and probabilistic. In the adversarial model, each node has a weight (higher weight implying higher reliability) and the adversary can remove any subset of nodes of total weight at most a given bound W and our goal is to find a placement that incurs the least disruption against such an adversary. In the probabilistic model, each node has a probability of failure and we need to find a placement that maximizes the probability that at least K out of N tasks survive at any time. For adversarial failures, we first show that (i) the problems are in Σ2, the second level of the polynomial hierarchy, (ii) a basic variant, that we call RobustFAP, is co-NPhard, and (iii) an all-or-nothing version of RobustFAP is Σ2-complete. We then give a PTAS for RobustFAP, a key ingredient of which is a solution that we design for a fractional version of RobustFAP. We then study fractional Ro-bustFAP over hierarchies, denoted HierRobustFAP, and introduce a notion of hierarchical max-min fairness and a novel Generalized Spreading algorithm which is simultaneously optimal for all W. These generalize the classical notion of max-min fairness to work with nodes of differing capacities, differing reliability weights and hierarchical structures. Using randomized rounding, we extend this to give an algorithm for integral HierRobustFAP. For the probabilistic version, we first give an algorithm that achieves an additive ε approximation in the failure probability for the single level version, called ProbFAP, while giving up a (1 + ε) multiplicative factor in the number of failures. We then extend the result to the hierarchical version, HierProbFAP, achieving an ε additive approximation * Supported in part by NSF grants CNS-1217981, CCF-1422715, and CCF-1535929, and a Google Research Award.

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Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems

Cited by 18 publications

References 46 publications

Maximizing expected utility over a knapsack constraint

Maximizing expected utility over a knapsack constraint

Robust and Probabilistic Failure-Aware Placement

Robust and Probabilistic Failure-Aware Placement

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