A note on Integer Linear Programming formulations for linear ordering problems on graphs

David Coudert 1
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this paper, we present a new set of constraints for modeling linear ordering problems on graphs using Integer Linear Programming (ILP). These constraints express the membership of a vertex to a prefix rather than the exact position of a vertex in the ordering. We use these constraints to propose new ILP formulations for well-known linear ordering optimization problems, namely the Pathwidth, Cutwidth, Bandwidth, SumCut and Optimal Linear Arrangement problems. Our formulations are not only more compact than previous proposals, but also more efficient as shown by our experimental evaluations on large benchmark instances.
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Submitted on : Tuesday, February 9, 2016 - 4:47:02 PM
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David Coudert. A note on Integer Linear Programming formulations for linear ordering problems on graphs. [Research Report] Inria; I3S; Universite Nice Sophia Antipolis; CNRS. 2016, pp.33. ⟨hal-01271838⟩

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