Markov chains and optimality of the Hamiltonian cycle


Litvak, Nelly and Ejov, Vladimir (2009) Markov chains and optimality of the Hamiltonian cycle. Mathematics of Operations Research, 34 (1). pp. 71-82. ISSN 0364-765X

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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.
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Metis ID: 263887