Hedging Uncertainty: Approximation Algorithms for Stochastic Optimization Problems

We study two-stage, finite-scenario stochastic versions of several combinatorial optimization problems, and provide nearly tight approximation algorithms for them. Our problems range from the graph-theoretic (shortest path, vertex cover, facility location) to set-theoretic (set cover, bin packing),...

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Vydáno v:	Mathematical programming Ročník 108; číslo 1; s. 97 - 114
Hlavní autoři:	Ravi, R., Sinha, Amitabh
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Heidelberg Springer 01.08.2006 Springer Nature B.V
Témata:	Algorithms Applied sciences Approximation Decision making Exact sciences and technology Flows in networks. Combinatorial problems Graph theory Hedging Integer programming Linear programming Logistics Mathematical programming Operational research and scientific management Operational research. Management science Optimization Probability distribution Set theory Stochastic models Studies Variables Graph path Combinatorial problem Rounding error Stochastic approximation Vertex(graph) Approximation algorithm Combinatorial optimization Location problem Facility location Uncertain system 20G40 20C20 Set covering 20E28 Mathematical programming Lp approximation Script Warranty Probabilistic approach Shortest path Bin packing problem Graph theory Stochastic programming Primal dual method Greedy algorithm Bin packing Set theory
ISSN:	0025-5610, 1436-4646
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Abstract	We study two-stage, finite-scenario stochastic versions of several combinatorial optimization problems, and provide nearly tight approximation algorithms for them. Our problems range from the graph-theoretic (shortest path, vertex cover, facility location) to set-theoretic (set cover, bin packing), and contain representatives with different approximation ratios. The approximation ratio of the stochastic variant of a typical problem is found to be of the same order of magnitude as its deterministic counterpart. Furthermore, we show that common techniques for designing approximation algorithms such as LP rounding, the primal-dual method, and the greedy algorithm, can be adapted to obtain these results. [PUBLICATION ABSTRACT]
AbstractList	We study two-stage, finite-scenario stochastic versions of several combinatorial optimization problems, and provide nearly tight approximation algorithms for them. Our problems range from the graph-theoretic (shortest path, vertex cover, facility location) to set-theoretic (set cover, bin packing), and contain representatives with different approximation ratios. The approximation ratio of the stochastic variant of a typical problem is found to be of the same order of magnitude as its deterministic counterpart. Furthermore, we show that common techniques for designing approximation algorithms such as LP rounding, the primal-dual method, and the greedy algorithm, can be adapted to obtain these results. [PUBLICATION ABSTRACT]
Author	Sinha, Amitabh Ravi, R.
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Keywords	Graph path Combinatorial problem Rounding error Stochastic approximation Vertex(graph) Approximation algorithm Combinatorial optimization Location problem Facility location Uncertain system 20G40 20C20 Set covering 20E28 Mathematical programming Lp approximation Script Warranty Probabilistic approach Shortest path Bin packing problem Graph theory Stochastic programming Primal dual method Greedy algorithm Bin packing Set theory
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SubjectTerms	Algorithms Applied sciences Approximation Decision making Exact sciences and technology Flows in networks. Combinatorial problems Graph theory Hedging Integer programming Linear programming Logistics Mathematical programming Operational research and scientific management Operational research. Management science Optimization Probability distribution Set theory Stochastic models Studies Variables
Title	Hedging Uncertainty: Approximation Algorithms for Stochastic Optimization Problems
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