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Stochastic packing integer programs with few queries

  • Takanori Maehara
  • Yutaro YamaguchiEmail author
Full Length Paper Series A
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Abstract

We consider a stochastic variant of the packing-type integer linear programming problem, which contains random variables in the objective vector. We are allowed to reveal each entry of the objective vector by conducting a query, and the task is to find a good solution by conducting a small number of queries. We propose a general framework of adaptive and non-adaptive algorithms for this problem, and provide a unified methodology for analyzing the performance of those algorithms. We also demonstrate our framework by applying it to a variety of stochastic combinatorial optimization problems such as matching, matroid, and stable set problems.

Keywords

Stochastic problems with queries Packing problems Linear programming (LP) LP duality Approximation algorithms 

Mathematics Subject Classification

90C15 90C05 05C70 05B35 68W20 68W25 

Notes

Acknowledgements

The authors thank anonymous reviewers for their careful reading and a number of valuable comments. This work was supported by JSPS KAKENHI Grant Numbers 16H06931 and 16K16011.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2019

Authors and Affiliations

  1. 1.Osaka UniversitySuitaJapan
  2. 2.RIKEN Center for Advanced Intelligence ProjectTokyoJapan

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