When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Greedy strikes back: improved facility location algorithms
Journal of Algorithms
Approximation in stochastic scheduling: the power of LP-based priority policies
Journal of the ACM (JACM)
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Applications of approximation algorithms to cooperative games
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms
Some optimal inapproximability results
Journal of the ACM (JACM)
Allocating Bandwidth for Bursty Connections
SIAM Journal on Computing
The Sample Average Approximation Method for Stochastic Discrete Optimization
SIAM Journal on Optimization
Approximation Hardness of the Steiner Tree Problem on Graphs
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
SIAM Journal on Computing
Stochastic Load Balancing and Related Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Group Strategyproof Mechanisms via Primal-Dual Algorithms
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
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
Stochastic Machine Scheduling with Precedence Constraints
SIAM Journal on Computing
Network design for information networks
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
Hedging Uncertainty: Approximation Algorithms for Stochastic Optimization Problems
Mathematical Programming: Series A and B
Computational complexity of stochastic programming problems
Mathematical Programming: Series A and B
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
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
A Group-Strategyproof Cost Sharing Mechanism for the Steiner Forest Game
SIAM Journal on Computing
Limitations of cross-monotonic cost-sharing schemes
ACM Transactions on Algorithms (TALG)
Equitable Cost Allocations via Primal-Dual-Type Algorithms
SIAM Journal on Computing
Infrastructure Leasing Problems
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
LP Rounding Approximation Algorithms for Stochastic Network Design
Mathematics of Operations Research
Strategyproof cost-sharing mechanisms for set cover and facility location games
Decision Support Systems - Special issue: The fourth ACM conference on electronic commerce
Strict Cost Sharing Schemes for Steiner Forest
SIAM Journal on Computing
Stochastic steiner trees without a root
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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 vehicle routing with recourse
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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We consider two- and multistage versions of stochastic combinatorial optimization problems with recourse: in this framework, the instance for the combinatorial optimization problem is drawn from a known probability distribution $\pi$ and is only revealed to the algorithm over two (or multiple) stages. At each stage, on receiving some more information about the instance, the algorithm is allowed to build some partial solution. Since the costs of elements increase with each passing stage, there is a natural tension between waiting for later stages, to gain more information about the instance, and purchasing elements in earlier stages, to take advantages of lower costs. We provide approximation algorithms for stochastic combinatorial optimization problems (such as the Steiner tree problem, the Steiner network problem, and the vertex cover problem) by means of a simple sampling-based algorithm. In every stage, our algorithm samples the probability distribution of the requirements and constructs a partial solution to serve the resulting sample. We show that if one can construct cost-sharing functions associated with the algorithms used to construct these partial solutions, then this strategy results in provable approximation guarantees for the overall stochastic optimization problem. We also extend this approach to provide an approximation algorithm for the stochastic version of the uncapacitated facility location problem, a problem that does not fit into the simpler framework of our main model.