… 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 process that …

… a set of Markov chains corresponding to a given graph. We prove that Hamiltonian cycles are
… Such sensitivity finds its explanation in the theory of singularly perturbed Markov chains. A …

… In the present approach, we embed a given graph in a singularly perturbed MDP in such
a way that we can identify Hamiltonian cycles with irreducible Markov chains and sub-cycles …

… We shall now consider the Hamiltonian cycle problem. It would be … In graph theoretic terms,
the problem is to find a simple cycle … Observe that / also induces a Markov chain with the …

… in a singularly perturbed MDP in such a way that we can identify Hamiltonian cycles with
irreducible Markov chains and … Indirectly, this allows us to search for a Hamiltonian cycle in the …

… the Hamiltonian cycle problem embedded in a singularly perturbed Markov decision process…
We emphasize that the perturbation is chosen to ensure that the Markov chain defined by P, …

… They conjectured that the optimality of Hamiltonian cycles for the trace function still holds
over the set of Markov chains when we apply a singular perturbation to the Markov chains …

… We consider a singularly perturbed (finite state) Markov chain … the singular part is obtained
via a reduction process similar to … Markov chains of much smaller dimension than the original …

… In the present approach, we embedded a given graph in a singularly perturbed MDP in
such a way that we can identify Hamiltonian Cycles with irreducible Markov chains and sub…

… Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a
diffusion process on the graph… Its characteristics are expressed through the Hamiltonian and the …