SIAM Journal on Discrete Mathematics
Annals of Operations Research
A Monge property for the d-dimensional transportation problem
Proceedings of the workshop on Discrete algorithms
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
Allocating bandwidth for bursty connections
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Mathematics of Operations Research
Approximation in stochastic scheduling: the power of LP-based priority policies
Journal of the ACM (JACM)
The Sample Average Approximation Method for Stochastic Discrete Optimization
SIAM Journal on Optimization
A d/2 approximation for maximum weight independent set in d-claw free graphs
Nordic Journal of Computing
Group Strategyproof Mechanisms via Primal-Dual Algorithms
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Cross-monotonic cost-sharing methods for connected facility location games
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Operations Research
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Probabilistic Combinatorial Optimization: Moments, Semidefinite Programming, and Asymptotic Bounds
SIAM Journal on Optimization
Optimal Inequalities in Probability Theory: A Convex Optimization Approach
SIAM Journal on Optimization
A group-strategyproof mechanism for Steiner forests
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Sampling-based Approximation Algorithms for Multi-stage Stochastic
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Worst-case distribution analysis of stochastic programs
Mathematical Programming: Series A and B
On the complexity of approximating k-set packing
Computational Complexity
Expected Value of Distribution Information for the Newsvendor Problem
Operations Research
Robust Mean-Covariance Solutions for Stochastic Optimization
Operations Research
Algorithmic Game Theory
Limitations of cross-monotonic cost-sharing schemes
ACM Transactions on Algorithms (TALG)
Optimal approximation for the submodular welfare problem in the value oracle model
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
A Robust Optimization Perspective on Stochastic Programming
Operations Research
Distributionally Robust Optimization and Its Tractable Approximations
Operations Research
Correlation robust stochastic optimization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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
Game Theoretical Approach for Reliable Enhanced Indexation
Decision Analysis
Mechanism design for a risk averse seller
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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When decisions are made in the presence of high-dimensional stochastic data, handling joint distribution of correlated random variables can present a formidable task, both in terms of sampling and estimation as well as algorithmic complexity. A common heuristic is to estimate only marginal distributions and substitute joint distribution by independent (product) distribution. In this paper, we study possible loss incurred on ignoring correlations through a distributionally robust stochastic programming model, and we quantify that loss as price of correlations (POC). Using techniques of cost sharing from game theory, we identify a wide class of problems for which POC has a small upper bound. To our interest, this class will include many stochastic convex programs, uncapacitated facility location, Steiner tree, and submodular functions, suggesting that the intuitive approach of assuming independent distribution acceptably approximates the robust model for these stochastic optimization problems. Additionally, we demonstrate hardness of bounding POC via examples of subadditive and supermodular functions that have large POC. We find that our results are also useful for solving many deterministic optimization problems like welfare maximization, k-dimensional matching, and transportation problems, under certain conditions.