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Journal of Algorithms and Computation
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December 2013, Page 1-81
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Gismondi, S. (2013). Modelling Decision Problems Via Birkhoff Polyhedra. Journal of Algorithms and Computation, 44(1), 61-81.
Stephen J. Gismondi. "Modelling Decision Problems Via Birkhoff Polyhedra". Journal of Algorithms and Computation, 44, 1, 2013, 61-81.
Gismondi, S. (2013). 'Modelling Decision Problems Via Birkhoff Polyhedra', Journal of Algorithms and Computation, 44(1), pp. 61-81.
Gismondi, S. Modelling Decision Problems Via Birkhoff Polyhedra. Journal of Algorithms and Computation, 2013; 44(1): 61-81.

Modelling Decision Problems Via Birkhoff Polyhedra

Article 5, Volume 44, Issue 1, December 2013, Page 61-81  XML PDF (1.68 MB)
Document Type: Research Paper
Author
Stephen J. Gismondi email
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
Combinatorial optimization; linear programming
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