Computing the 1-width of the incidence matrix of a Steiner Triple System gives rise to small set covering instances that provide a computational challenge for integer programming techniques. One major source of difficulty for instances of this family is their highly symmetric structure, which impairs the performance of most branch-and-bound algorithms. The largest instance in the family that has been solved corresponds to a Steiner Tripe System of order 81. We present optimal solutions to the set covering problems associated with systems of orders 135 and 243. The solutions are obtained by a tailored implementation of constraint orbital branching, a method for branching on general disjunctions designed to exploit symmetry in integer programs.

Solving Steiner Triple Covering Problems

ROSSI, FABRIZIO;SMRIGLIO, STEFANO
2010-01-01

Abstract

Computing the 1-width of the incidence matrix of a Steiner Triple System gives rise to small set covering instances that provide a computational challenge for integer programming techniques. One major source of difficulty for instances of this family is their highly symmetric structure, which impairs the performance of most branch-and-bound algorithms. The largest instance in the family that has been solved corresponds to a Steiner Tripe System of order 81. We present optimal solutions to the set covering problems associated with systems of orders 135 and 243. The solutions are obtained by a tailored implementation of constraint orbital branching, a method for branching on general disjunctions designed to exploit symmetry in integer programs.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/32621
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