Solving large Steiner Triple Covering Problems

Authors:
James Ostrowski;Jeff Linderoth;Fabrizio Rossi;Stefano Smriglio
Affiliations:
Department of Management Sciences, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1;Department of Industrial and Systems Engineering, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706, USA;Dipartimento di Informatica, Universití di L'Aquila, Via Vetoio I-67010 Coppito (AQ), Italy;Dipartimento di Informatica, Universití di L'Aquila, Via Vetoio I-67010 Coppito (AQ), Italy
Venue:
Operations Research Letters
Year:
2011

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Abstract

Computing the 1-width of the incidence matrix of a Steiner Triple System gives rise to highly symmetric and computationally challenging set covering problems. The largest instance solved so far corresponds to a Steiner Tripe System of order 81. We present optimal solutions for systems of orders 135 and 243. These are computed by a tailored implementation of constraint orbital branching, a method designed to exploit symmetry in integer programs.