Linear Programming Based Algorithms

Vivek S. Borkar (), Vladimir Ejov (), Jerzy A. Filar () and Giang T. Nguyen ()
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Vivek S. Borkar: IIT, Powai
Vladimir Ejov: Flinders University
Jerzy A. Filar: Flinders University
Giang T. Nguyen: Université libre de Bruxelles

Chapter Chapter 7 in Hamiltonian Cycle Problem and Markov Chains, 2012, pp 113-142 from Springer

Abstract: Abstract In Chapter 4, we showed that when a graph is embedded in a suitably constructed Markov decision process, the associated convex domain of discounted occupational measures is a polyhedron with extreme points corresponding to all spanning subgraphs of the given graph. Furthermore, from Theorem 4.1 we learned that a simple cut of the above domain yields a polyhedron the extreme points of which correspond to only two possible types: Hamiltonian cycles and convex combinations of short and noose cycles. These properties, naturally, suggest certain algorithmic approaches to searching for Hamiltonian cycles.

Keywords: Extreme Point; Markov Decision Process; Hamiltonian Cycle; Positive Entry; Hamiltonian Graph (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-3232-6_7

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