Modelling Decision Problems Via Birkhoff Polyhedra

Document Type : Research Paper

Author

Department of Mathematics & Statistics, University of Guelph, Guelph, ON, CA. N1G 2W1

Abstract

A compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. Directed Hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. Sets of extrema of Birkhoff polyhedra are mapped to tours neither in a graph nor its complement and these sets are embedded into disjoint orthogonal spaces as the solution set of a compact formulation. An orthogonal projection of its solution set into the subspace spanned by the Birkhoff polytope is the convex hull of all tours neither in a graph nor its complement. It’s suggested that these techniques might be adaptable for application to linear programming models of network and path problems.

Keywords

Journal of Algorithms and Computation
Volume 44, Issue 1 - Serial Number 1
December 2013
Pages 61-81

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