TY - JOUR
T1 - Approximation algorithms for the covering-type k-violation linear program
AU - Takazawa, Yotaro
AU - Mizuno, Shinji
AU - Kitahara, Tomonari
N1 - Funding Information:
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.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
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.
UR - http://www.scopus.com/inward/record.url?scp=85064527095&partnerID=8YFLogxK
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 -