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Linear Programming Based Algorithms

In: Hamiltonian Cycle Problem and Markov Chains

Author

Listed:
  • Vivek S. Borkar

    (IIT, Powai)

  • Vladimir Ejov

    (Flinders University)

  • Jerzy A. Filar

    (Flinders University)

  • Giang T. Nguyen

    (Université libre de Bruxelles)

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.

Suggested Citation

  • Vivek S. Borkar & Vladimir Ejov & Jerzy A. Filar & Giang T. Nguyen, 2012. "Linear Programming Based Algorithms," International Series in Operations Research & Management Science, in: Hamiltonian Cycle Problem and Markov Chains, edition 127, chapter 0, pages 113-142, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-3232-6_7
    DOI: 10.1007/978-1-4614-3232-6_7
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