Hamiltonian cycles and Markov chains
Mathematics of Operations Research
Constrained Discounted Markov Decision Processes and Hamiltonian Cycles
Mathematics of Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Controlled Markov chains, graphs, and Hamiltonicity
Foundations and Trends® in Stochastic Systems
Simulation and the Monte Carlo Method (Wiley Series in Probability and Statistics)
Simulation and the Monte Carlo Method (Wiley Series in Probability and Statistics)
Markov Chains and Optimality of the Hamiltonian Cycle
Mathematics of Operations Research
On the Hamiltonicity Gap and doubly stochastic matrices
Random Structures & Algorithms
Refined MDP-Based Branch-and-Fix Algorithm for the Hamiltonian Cycle Problem
Mathematics of Operations Research
An asymptotic simplex method for singularly perturbed linear programs
Operations Research Letters
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We develop a new, random walk-based, algorithm for the Hamiltonian cycle problem. The random walk is on pairs of extreme points of two suitably constructed polytopes. The latter are derived from geometric properties of the space of discounted occupational measures corresponding to a given graph. The algorithm searches for a measure that corresponds to a common extreme point in these two specially constructed polyhedral subsets of that space. We prove that if a given undirected graph is Hamiltonian, then with probability one this random walk algorithm detects its Hamiltonicity in a finite number of iterations. We support these theoretical results by numerical experiments that demonstrate a surprisingly slow growth in the required number of iterations with the size of the given graph.