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Author Shmoys, David B. ♦ Swamy, Chaitanya
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2006
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Approximation algorithms ♦ Convex optimization ♦ Randomized algorithms
Abstract Stochastic optimization problems attempt to model uncertainty in the data by assuming that the input is specified by a probability distribution. We consider the well-studied paradigm of 2-stage models with recourse: first, given only distributional information about (some of) the data one commits on initial actions, and then once the actual data is realized (according to the distribution), further (recourse) actions can be taken. We show that for a broad class of 2-stage linear models with recourse, one can, for any ε > 0, in time polynomial in 1/ε and the size of the input, compute a solution of value within a factor (1+ε) of the optimum, in spite of the fact that exponentially many second-stage scenarios may occur. In conjunction with a suitable rounding scheme, this yields the first approximation algorithms for 2-stage stochastic integer optimization problems where the underlying random data is given by a “black box” and no restrictions are placed on the costs in the two stages. Our rounding approach for stochastic integer programs shows that an approximation algorithm for a deterministic analogue yields, with a small constant-factor loss, provably near-optimal solutions for the stochastic generalization. Among the range of applications, we consider are stochastic versions of the multicommodity flow, set cover, vertex cover, and facility location problems.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2006-11-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 53
Issue Number 6
Page Count 35
Starting Page 978
Ending Page 1012

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Source: ACM Digital Library