Two Computationally Difficult Set Covering Problems that Arise in Computing the 1-Width of Incidence Matrices of Steiner Triple Systems.

摘要

Two minimum cardinality set covering problems of similar structure are presented as difficult test problems for evaluating the computational efficiency of integer programming and set covering algorithms. The smaller problem has 117constraints and 27variables and the larger one,constructed by H.J. Ryser,has 330constraints and 45variables. The constraint matrices of the two set covering problems are incidence matrices of Steiner triple systems. An optimal solution to the problem that the authors were able to solve (the smaller one) gives some new information on the 1-widths of members of this class of (0,1)-matrices. (Author)