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

Yotaro Takazawa, Shinji Mizuno, Tomonari Kitahara

Research output: Contribution to journalArticle


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 languageEnglish
Pages (from-to)1515-1521
Number of pages7
JournalOptimization Letters
Issue number7
Publication statusPublished - Oct 1 2019


All Science Journal Classification (ASJC) codes

  • Control and Optimization

Cite this