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

mathematics and information

Research output: Contribution to journal › Article

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
Journal	Optimization Letters
DOIs	https://doi.org/10.1007/s11590-019-01425-w
Publication status	Published - Jan 1 2019

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LP Relaxation

Linear Program

Approximation Algorithms

Covering

Mixed Integer Program

Integrality

NP-complete problem

Lower bound

Imply

All Science Journal Classification (ASJC) codes

Control and Optimization

Cite this

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

Approximation algorithms for the covering-type k-violation linear program. / Takazawa, Yotaro; Mizuno, Shinji; Kitahara, Tomonari.

In: Optimization Letters, 01.01.2019.

Research output: Contribution to journal › Article

Takazawa, Y, Mizuno, S & Kitahara, T 2019, 'Approximation algorithms for the covering-type k-violation linear program', Optimization Letters. https://doi.org/10.1007/s11590-019-01425-w

Takazawa Y, Mizuno S, Kitahara T. Approximation algorithms for the covering-type k-violation linear program. Optimization Letters. 2019 Jan 1. https://doi.org/10.1007/s11590-019-01425-w

Takazawa, Yotaro ; Mizuno, Shinji ; Kitahara, Tomonari. / Approximation algorithms for the covering-type k-violation linear program. In: Optimization Letters. 2019.

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