Set Covering by an All Integer Algorithm

Abstract

Computational experience with a modified linear programming method for the inequality or equality set covering problem (i.e. minimize cx subject to Ex ≥ e or Ex = e , x _i = 0 or 1, where E is a zero-one matrix, e is a column of ones, and c is a nonnegative integral row) is presented. The zero-one composition of the constraint matrix and the right-hand side of ones suggested an algorithm in which dual simplex iterations are performed whenever unit pivots are available and Gomory all integer cuts are adjoined when they are not. Applications to enumerative and heuristic schemes are also discussed.