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Approximation algorithms for the covering-type k-violation linear program

  • Yotaro TakazawaEmail author
  • Shinji Mizuno
  • Tomonari Kitahara
Original Paper
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Abstract

We study the covering-type k-violation linear program where at most k of the constraints can be violated. This problem is formulated as a mixed integer program and known to be strongly NP-hard. In this paper, we present a simple \((k+1)\)-approximation algorithm using a natural LP relaxation. We also show that the integrality gap of the LP relaxation is \(k+1\). This implies we can not get better approximation algorithms when we use the LP-relaxation as a lower bound of the optimal value.

Keywords

Approximation algorithms Mixed integer program k-violation linear program Linear relaxation Rounding algorithm 

Notes

Acknowledgements

We thank the anonymous referees for their helpful comments and suggestions. This research is supported in part by Grant-in-Aid for Science Research (A) 26242027 of Japan Society for the Promotion of Science and Grant-in-Aid for Young Scientist (B) 15K15941.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Industrial Engineering and EconomicsTokyo Institute of TechnologyTokyoJapan

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