Solving large Steiner Triple Covering Problems

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...

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Veröffentlicht in:	Operations research letters 2011-03, Vol.39 (2), p.127-131
Hauptverfasser:	Ostrowski, James, Linderoth, Jeff, Rossi, Fabrizio, Smriglio, Stefano
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Branch-and-bound algorithms Computation Covering Exact sciences and technology Flows in networks. Combinatorial problems Incidence Integer programming Integers Mathematical models Mathematical programming Operational research and scientific management Operational research. Management science Operations research Optimization Orbitals Steiner Triple Systems Symmetry
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Zusammenfassung:	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.
ISSN:	0167-6377 1872-7468
DOI:	10.1016/j.orl.2011.02.001