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Please use this identifier to cite or link to this item: http://hdl.handle.net/2328/26400

Title: Hamiltonian cycles and singularly perturbed Markov chains
Authors: Ejov, Vladimir
Filar, Jerzy A
Nguyen, Minh-Tuan
Keywords: Mathematics
Hamiltonian cycle problem
Markov decision process
Issue Date: 2004
Publisher: INFORMS
Citation: Ejov, V., Filar, J.A. and Nguyen, M.T., 2004. Hamiltonian cycles and singularly perturbed Markov chains. Mathematics of Operations Research, 29(1), 114-131.
Abstract: We consider the Hamiltonian cycle problem embedded in a singularly perturbed Markov decision process. We also consider a functional on the space of deterministic policies of the process that consist of the (1,1)-entry of the fundamental matrices of the Markov chains induced by the same policies. We show that when the perturbation parameter, e, is less than or equal to 1/N2, the Hamiltonian cycles of the directed graph are precisely the minimizers of our functional over the space of deterministic policies. In the process, we derive analytical expressions for the possible N distinct values of the functional over the, typically, much larger space of deterministic policies.
URI: http://hdl.handle.net/2328/26400
ISSN: 0364-765X
Appears in Collections:Computer Science, Engineering and Mathematics - Collected Works

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