ARC reduction and path preference in stochastic acyclic networks
Management Science
Random pseudo-polynomial algorithms for exact matroid problems
Journal of Algorithms
Allocating bandwidth for bursty connections
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On multi-dimensional packing problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Stochastic Load Balancing and Related Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Adaptivity and approximation for stochastic packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Multicriteria Global Minimum Cuts
Algorithmica
Stochastic shortest paths via Quasi-convex maximization
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Matroids, secretary problems, and online mechanisms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computing Equilibria in Anonymous Games
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A Knapsack Secretary Problem with Applications
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Automated online mechanism design and prophet inequalities
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Multi-parameter mechanism design and sequential posted pricing
Proceedings of the forty-second ACM symposium on Theory of computing
Approximation algorithms for reliable stochastic combinatorial optimization
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Bayesian Combinatorial Auctions: Expanding Single Buyer Mechanisms to Many Buyers
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Approximation Algorithms for Correlated Knapsacks and Non-martingale Bandits
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Improved competitive ratio for the matroid secretary problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Multi-budgeted matchings and matroid intersection via dependent rounding
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Secretary problems: laminar matroid and interval scheduling
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Improved approximation results for stochastic knapsack problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
When LP Is the Cure for Your Matching Woes: Improved Bounds for Stochastic Matchings
Algorithmica - Special Issue: Algorithm Design and Analysis
A PTAS for the chance-constrained knapsack problem with random item sizes
Operations Research Letters
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We study several stochastic combinatorial problems, including the expected utility maximization problem, the stochastic knapsack problem and the stochastic bin packing problem. A common technical challenge in these problems is to optimize some function (other than the expectation) of the sum of a set of random variables. The difficulty is mainly due to the fact that the probability distribution of the sum is the convolution of a set of distributions, which is not an easy objective function to work with. To tackle this difficulty, we introduce the Poisson approximation technique. The technique is based on the Poisson approximation theorem discovered by Le Cam, which enables us to approximate the distribution of the sum of a set of random variables using a compound Poisson distribution. Using the technique, we can reduce a variety of stochastic problems to the corresponding deterministic multiple-objective problems, which either can be solved by standard dynamic programming or have known solutions in the literature. For the problems mentioned above, we obtain the following results: We first study the expected utility maximization problem introduced recently [Li and Despande, FOCS11]. For monotone and Lipschitz utility functions, we obtain an additive PTAS if there is a multidimensional PTAS for the multi-objective version of the problem, strictly generalizing the previous result. The result implies the first additive PTAS for maximizing threshold probability for the stochastic versions of global min-cut, matroid base and matroid intersection. For the stochastic bin packing problem (introduced in [Kleinberg, Rabani and Tardos, STOC97]), we show there is a polynomial time algorithm which uses at most the optimal number of bins, if we relax the size of each bin and the overflow probability by e for any constant ε0. Based on this result, we obtain a 3-approximation if only the size of each bin can be relaxed by ε, improving the known O(1/ε) factor for constant overflow probability. For stochastic knapsack, we show a (1+ε)-approximation using ε extra capacity for any ε0, even when the size and reward of each item may be correlated and cancelations of items are allowed. This generalizes the previous work [Balghat, Goel and Khanna, SODA11] for the case without correlation and cancelation. Our algorithm is also simpler. We also present a factor 2+ε approximation algorithm for stochastic knapsack with cancelations, for any constant ε0, improving the current known approximation factor of 8 [Gupta, Krishnaswamy, Molinaro and Ravi, FOCS11]. We also study an interesting variant of the stochastic knapsack problem, where the size and the profit of each item are revealed before the decision is made. The problem falls into the framework of Bayesian online selection problems, which has been studied a lot recently.