Hamiltonian cycles and Markov chains
Mathematics of Operations Research
Constrained discounted dynamic programming
Mathematics of Operations Research
Competitive Markov decision processes
Competitive Markov decision processes
Graph theory and its applications
Graph theory and its applications
Constrained Discounted Markov Decision Processes and Hamiltonian Cycles
Mathematics of Operations Research
An Interior Point Heuristic for the Hamiltonian Cycle Problem via Markov Decision Processes
Journal of Global Optimization
Graph Theory With Applications
Graph Theory With Applications
Applied Combinatorics
Controlled Markov chains, graphs, and Hamiltonicity
Foundations and Trends® in Stochastic Systems
Fast generation of regular graphs and construction of cages
Journal of Graph Theory
Controlled Markov chains, graphs, and Hamiltonicity
Foundations and Trends® in Stochastic Systems
Hamiltonian Cycles, Random Walks, and Discounted Occupational Measures
Mathematics of Operations Research
Splitting Randomized Stationary Policies in Total-Reward Markov Decision Processes
Mathematics of Operations Research
Markov chains, Hamiltonian cycles and volumes of convex bodies
Journal of Global Optimization
Hi-index | 0.00 |
We consider the famous Hamiltonian cycle problem (HCP) embedded in a Markov decision process (MDP). More specifically, we consider the HCP as an optimisation problem over the space of occupation measures induced by the MDP's stationary policies. In recent years, this approach to the HCP has led to a number of alternative formulations and algorithmic approaches. In this paper, we focus on a specific embedding, because of the work of Feinberg. We present a “branch-and-fix” type algorithm that solves the HCP. At each branch of the algorithm, only a linear program needs to be solved and the dimensions of the successive linear programs are shrinking rather than expanding. Because the nodes of the branch-and-fix tree correspond to specially structured 1-randomised policies, we characterise the latter. This characterisation indicates that the total number of such policies is significantly smaller than the subset of all 1-randomised policies. Finally, we present some numerical results.