Markov chains and optimality of the Hamiltonian cycle

Nelli Litvak, Vladimir Ejov

Research output: Contribution to journalArticleAcademicpeer-review

8 Citations (Scopus)

Abstract

We consider the Hamiltonian cycle problem (HCP) embedded in a controlled Markov decision process. In this setting, HCP reduces to an optimization problem on a set of Markov chains corresponding to a given graph. We prove that Hamiltonian cycles are minimizers for the trace of the fundamental matrix on a set of all stochastic transition matrices. In case of doubly stochastic matrices with symmetric linear perturbation, we show that Hamiltonian cycles minimize a diagonal element of a fundamental matrix for all admissible values of the perturbation parameter. In contrast to the previous work on this topic, our arguments are primarily based on probabilistic rather than algebraic methods.
Original languageUndefined
Article number10.1287/moor.1080.0351
Pages (from-to)71-82
Number of pages12
JournalMathematics of operations research
Volume34
Issue number1
DOIs
Publication statusPublished - 27 Jan 2009

Keywords

  • IR-67701
  • METIS-263887
  • MSC-60J10
  • EWI-15437
  • Singular perturbation
  • Hamiltonian cycle
  • Fundamental matrix
  • Markov chains

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