Approximating Bounded 0-1 Integer Linear Programs (Extended Abstract)

The problem of finding approximate solutions for a subclass of 0-1 integer linear programming denoted by ILP(k,p) is considered. The problem involves finding X E {0,1}" that minimizes cjXj subject to the con- straint AX 2 p . l,, where A is a 0-1 m x n matrix with at most k 1's per row, and 1, is the all-1 m-vector. This is a MAX-SNP-hard problem, and special cases include, for example, the Bounded Set Cover problem when p = 1, and the Vertex Cover problem when k = 2 and p = 1. Several deterministic approximation algorithms are presented, all with approximation ratios of k -p+ 1, which is Constant when the difference k - p is bounded. This naturally applies in the common case when both k and p are bounded, and is asymptotically better than the ln(mp) ratio guaranteed by the greedy heuristic.