The partial covering 0-1 integer program (PCIP) is a relaxed problem of the covering 0-1 integer program (CIP) such that some fixed number of constraints may not be satisfied. This type of relaxation is also discussed in the partial set multi-cover problem (PSMCP) and the partial set cover problem (PSCP). In this paper, we propose an approximation algorithm for PCIP by extending an approximation algorithm for PSCP by Gandhi et al. (2004).
to appear in department of Industrial Engineering and Economics Working Paper, Tokyo Institute of Technology.