This research monograph summarizes a line of research that maps certain classical
problems of discrete mathematics and operations research-such as the Hamiltonian Cycle …

This manuscript summarizes a line of research that maps certain classical problems of
discrete mathematics—such as the Hamiltonian Cycle and the Traveling Salesman …

In this paper, we present some algebraic properties of a particular class of probability
transition matrices, namely, Hamiltonian transition matrices. Each matrix PP in this class …

In this paper we derive new characterizations of the Hamiltonian cycles of a directed graph,
and a new LP-relaxation of the Traveling Salesman Problem. Our results are obtained via an …

We consider the Hamiltonian cycle problem on a given graph G. With such a graph we can
associate a family F of probability transition matrices of Markov chains whose entries …

Given a directed graph and a given starting node, the Hamiltonian Cycle Problem (HCP) is
to find a path that visits every other node exactly once before returning to the starting node …

We consider the Hamiltonian cycle problem embedded in a singularly perturbed Markov
decision process. We also consider a functional on the space of deterministic policies of the …

This paper is a survey of various proofs of the so called {\em fundamental theorem of Markov
chains}: every ergodic Markov chain has a unique positive stationary distribution and the …

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 …

We consider the Hamiltonian cycle problem (HCP) embedded in a singularly perturbed
Markov decision process (MDP). More specifically, we consider the HCP as an optimization …