Approximation of a geometric set covering problem

Abstract

We consider a special set covering problem. This problem is a generalization of finding a minimum clique cover in an interval graph. When formulated as an integer program, the 0-1 constraint matrix of this integer program can be partitioned into an interval matrix and a special 0-1 matrix with a single 1 per column. We show that the value of this formulation is bounded by 2κκ/κ + 1 times the value of the LP-relaxation, where κ is the maximum row sum of the special matrix. For the "smallest" difficult case, i.e., κ = 2, this bound is tight. Also we provide an O(n) 3/2 -approximation algorithm in case κ = 2. © 2001 Springer Berlin Heidelberg.