Kalinowski, Thomas

Mohammadian, Sogol

2021-11

<p>We study a certain polytope depending on a graph G and a parameter <i>β</i> ∈ (0,1) that arises from embedding the Hamiltonian cycle problem in a discounted Markov decision process. Literature suggests a conjecture a lower bound on the proportion of feasible bases corresponding to Hamiltonian cycles in the set of all feasible bases. We make progress toward a proof of the conjecture by proving results about the structure of feasible bases. In particular, we prove three main results: (1) the set of feasible bases is independent of the parameter <i>β</i> when the parameter is close to one, (2) the polytope can be interpreted as a generalized network flow polytope, and (3) we deduce a combinatorial interpretation of the feasible bases. We also provide a full characterization for a special class of feasible bases, and we apply this to provide some computational support for the conjecture.</p>

Mathematics of Operations Research, 46(4), p. 1366-1389

1526-5471

0364-765X

https://hdl.handle.net/1959.11/30253

Institute for Operations Research and the Management Sciences (INFORMS)

Feasible Bases for a Polytope Related to the Hamilton Cycle Problem

Journal Article

Publication