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 using the LP-relaxation as a lower bound of the optimal value.
to appear in department of Industrial Engineering and Economics Working Paper, Tokyo Institute of Technology.