On the complexity of computing the volume of a polyhedron
SIAM Journal on Computing
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
Sensitivity of constrained Markov decision processes
Annals of Operations Research
Hamiltonian cycles and Markov chains
Mathematics of Operations Research
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
Simulated annealing in convex bodies and an O*(n4) volume algorithm
Journal of Computer and System Sciences - Special issue on FOCS 2003
Controlled Markov chains, graphs, and Hamiltonicity
Foundations and Trends® in Stochastic Systems
Refined MDP-Based Branch-and-Fix Algorithm for the Hamiltonian Cycle Problem
Mathematics of Operations Research
Hi-index | 0.00 |
In this note the Hamiltonian cycle problem is mapped into an infinite horizon discounted cost constrained Markov decision problem. The occupation measure based linear polytope associated with this control problem defines a convex set which either strictly contains or is equal to another convex set, depending on whether the underlying graph has a Hamiltonian cycle or not. This allows us to distinguish Hamiltonian graphs from non-Hamiltonian graphs by comparing volumes of two convex sets.