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

Yotaro Takazawa; Shinji Mizuno; Tomonari Kitahara

doi:10.1007/s11590-019-01425-w

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

Yotaro Takazawa, Shinji Mizuno, Tomonari Kitahara

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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.

Original language	English
Pages (from-to)	1515-1521
Number of pages	7
Journal	Optimization Letters
Volume	13
Issue number	7
DOIs	https://doi.org/10.1007/s11590-019-01425-w
Publication status	Published - Oct 1 2019

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All Science Journal Classification (ASJC) codes

Control and Optimization

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Takazawa, Y., Mizuno, S., & Kitahara, T. (2019). Approximation algorithms for the covering-type k-violation linear program. Optimization Letters, 13(7), 1515-1521. https://doi.org/10.1007/s11590-019-01425-w

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10.1007/s11590-019-01425-w