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Markov chains, Hamiltonian cycles and volumes of convex bodies

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  • Vivek Borkar
  • Jerzy Filar

Abstract

In this note the Hamiltonian cycle problem is mapped into an infinite horizon discounted cost constrained Markov decision problem. The occupation measure based linear polytope associated with this control problem defines a convex set which either strictly contains or is equal to another convex set, depending on whether the underlying graph has a Hamiltonian cycle or not. This allows us to distinguish Hamiltonian graphs from non-Hamiltonian graphs by comparing volumes of two convex sets. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Vivek Borkar & Jerzy Filar, 2013. "Markov chains, Hamiltonian cycles and volumes of convex bodies," Journal of Global Optimization, Springer, vol. 55(3), pages 633-639, March.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:3:p:633-639
    DOI: 10.1007/s10898-011-9819-6
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    References listed on IDEAS

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    1. Eugene A. Feinberg, 2000. "Constrained Discounted Markov Decision Processes and Hamiltonian Cycles," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 130-140, February.
    2. Jerzy A. Filar & Dmitry Krass, 1994. "Hamiltonian Cycles and Markov Chains," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 223-237, February.
    3. Vladimir Ejov & Jerzy A. Filar & Michael Haythorpe & Giang T. Nguyen, 2009. "Refined MDP-Based Branch-and-Fix Algorithm for the Hamiltonian Cycle Problem," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 758-768, August.
    4. T. P. I. Ahamed & V. S. Borkar & S. Juneja, 2006. "Adaptive Importance Sampling Technique for Markov Chains Using Stochastic Approximation," Operations Research, INFORMS, vol. 54(3), pages 489-504, June.
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