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 | |
| Publication status | Published - Oct 1 2019 |
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All Science Journal Classification (ASJC) codes
- Control and Optimization
Cite this
Approximation algorithms for the covering-type k-violation linear program. / Takazawa, Yotaro; Mizuno, Shinji; Kitahara, Tomonari.
In: Optimization Letters, Vol. 13, No. 7, 01.10.2019, p. 1515-1521.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Approximation algorithms for the covering-type k-violation linear program
AU - Takazawa, Yotaro
AU - Mizuno, Shinji
AU - Kitahara, Tomonari
PY - 2019/10/1
Y1 - 2019/10/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=85064527095&partnerID=8YFLogxK
U2 - 10.1007/s11590-019-01425-w
DO - 10.1007/s11590-019-01425-w
M3 - Article
AN - SCOPUS:85064527095
VL - 13
SP - 1515
EP - 1521
JO - Optimization Letters
JF - Optimization Letters
SN - 1862-4472
IS - 7
ER -