Hamiltonian cycles, quadratic programming, and ranking of extreme points
Recent advances in global optimization
Hamiltonian cycles and Markov chains
Mathematics of Operations Research
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Constrained Discounted Markov Decision Processes and Hamiltonian Cycles
Mathematics of Operations Research
Hamiltonian Cycles and Singularly Perturbed Markov Chains
Mathematics of Operations Research
An Interior Point Heuristic for the Hamiltonian Cycle Problem via Markov Decision Processes
Journal of Global Optimization
ACM Transactions on Internet Technology (TOIT)
Directed graphs, Hamiltonicity and doubly stochastic matrices
Random Structures & Algorithms
Controlled Markov chains, graphs, and Hamiltonicity
Foundations and Trends® in Stochastic Systems
On the Hamiltonicity Gap and doubly stochastic matrices
Random Structures & Algorithms
Hamiltonian Cycles, Random Walks, and Discounted Occupational Measures
Mathematics of Operations Research
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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.