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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Bibliographic Details
Published in:Mathematical programming Vol. 108; no. 1; pp. 97 - 114
Main Authors: Ravi, R., Sinha, Amitabh
Format: Journal Article
Language:English
Published: Heidelberg Springer 01.08.2006
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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]
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-005-0673-5