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Fooling Sets and the Spanning Tree Polytope

Kaveh Khoshkhah (khoshkhah***at***ut.ee)
Dirk Oliver Theis (dotheis***at***ut.ee)

Abstract: In the study of extensions of polytopes of combinatorial optimization problems, a notorious open question is that for the size of the smallest extended formulation of the Minimum Spanning Tree problem on a complete graph with n nodes. The best known lower bound is \Omega(n^2), the best known upper bound is O(n^3). In this note we show that the venerable fooling set method cannot be used to improve the lower bound: every fooling set for the Spanning Tree polytope has size O(n^2).

Keywords: extended formulations / extension complexity, spanning tree polytope, fooling sets

Category 1: Combinatorial Optimization (Polyhedra )

Category 2: Integer Programming (Other )


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Entry Submitted: 01/02/2017
Entry Accepted: 01/07/2017
Entry Last Modified: 01/24/2017

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