Operations Research
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Allocating Bandwidth for Bursty Connections
SIAM Journal on Computing
The Sample Average Approximation Method for Stochastic Discrete Optimization
SIAM Journal on Optimization
Stochastic Load Balancing and Related Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Improved Approximation Algorithms for the Uncapacitated Facility Location Problem
SIAM Journal on Computing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
An Edge in Time Saves Nine: LP Rounding Approximation Algorithms for Stochastic Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for clustering problems
Approximation algorithms for clustering problems
Sampling-based Approximation Algorithms for Multi-stage Stochastic
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
How to Pay, Come What May: Approximation Algorithms for Demand-Robust Covering Problems
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The prize-collecting generalized steiner tree problem via a new approach of primal-dual schema
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Hedging Uncertainty: Approximation Algorithms for Stochastic Optimization Problems
Mathematical Programming: Series A and B
Approximation algorithms for stochastic and risk-averse optimization
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Stochastic analyses for online combinatorial optimization problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Robust Combinatorial Optimization with Exponential Scenarios
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Two-Stage Robust Network Design with Exponential Scenarios
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
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
A constant approximation algorithm for the a priori traveling salesman problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
What about wednesday? approximation algorithms for multistage stochastic optimization
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Sampling bounds for stochastic optimization
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Stochastic combinatorial optimization with controllable risk aversion level
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Risk sensitivity of price of anarchy under uncertainty
Proceedings of the fourteenth ACM conference on Electronic commerce
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We consider various stochastic models that incorporate the notion of risk-averseness into the standard 2-stage recourse model, and develop novel techniques for solving the algorithmic problems arising in these models. A key notable feature of our work that distinguishes it from work in some other related models, such as the (standard) budget model and the (demand-) robust model, is that we obtain results in the black-box setting, that is, where one is given only sampling access to the underlying distribution. Our first model, which we call the risk-averse budget model, incorporates the notion of risk-averseness via a probabilistic constraint that restricts the probability (according to the underlying distribution) with which the second-stage cost may exceed a given budget B to at most a given input threshold ρ. We also a consider a closely-related model that we call the risk-averse robust model, where we seek to minimize the first-stage cost and the (1 − ρ)-quantile (according to the distribution) of the second-stage cost. We obtain approximation algorithms for a variety of combinatorial optimization problems including the set cover, vertex cover, multicut on trees, and facility location problems, in the risk-averse budget and robust models with black-box distributions. Our main contribution is to devise a fully polynomial approximation scheme for solving the LP-relaxations of a wide-variety of risk-averse budgeted problems. Complementing this, we give a simple rounding procedure that shows that one can exploit existing LP-based approximation algorithms for the 2-stage-stochastic and/or deterministic counterpart of the problem to round the fractional solution and obtain an approximation algorithm for the risk-averse problem. To the best of our knowledge, these are the first approximation results for problems involving probabilistic constraints and black-box distributions. A notable feature of our scheme is that it extends easily to handle a significantly richer class of risk-averse problems, where we impose a joint probabilistic budget constraint on different components of the second-stage cost. Consequently, we also obtain approximation algorithms in the setting where we have a joint budget constraint on different portions of the second-stage cost.