Zentralblatt MATH identifier Keywords Stochastic matrix Hamiltonian cycle perturbed Markov chain.
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More by Peter G. Abstract Article info and citation First page References Abstract We prove the conjecture formulated in Litvak and Ejov , namely, that the trace of the fundamental matrix of a singularly perturbed Markov chain that corresponds to a stochastic policy feasible for a given graph is minimised at policies corresponding to Hamiltonian cycles. Article information Source J.
Hamiltonian Cycle Problem and Markov Chains
Export citation. Export Cancel. References Andramonov, M. Hamiltonian cycle problem via Markov chains and min-type approaches. In Approximation and Complexity in Numerical Optimization , ed. The essence of HCP is contained in the following, deceptively simple, single sentence statement: given a graph on N nodes, find a simple cycle that contains all vertices of the graph Hamiltonian Cycle or prove that such a cycle does not exist The HCP is known to be NP-hard and has become a challenge that attracts mathematical minds both in its own right and because of its close relationship to the equally famous Traveling Salesman Problem TSP.
Hamiltonian Cycles and Singularly Perturbed Markov Chains
An efficient solution of the latter would have an enormous impact in operations research, optimization and computer science. However, from a mathematical perspective the underlying difficulty of the TSP is, perhaps, hidden in the Hamiltonian Cycle Problem that is the main focus here.
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Abstract This manuscript summarizes a line of research that maps certain classical problems of discrete mathematics — such as the Hamiltonian Cycle and the Traveling Salesman Problems — into convex domains where continuum analysis can be carried out. DOI: Book details.