Hamiltonian Cycles and Subsets of Discounted Occupational Measures

• 成果类型: Article
• 署名作者: Eshragh, Ali; Filar, Jerzy A.; Kalinowski, Thomas; Mohammadian, Sogol
• 署名单位: University of Newcastle; University of Queensland; University of New England
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2019.1009
• 发表日期: 2020
• 页码: 713-731
• 关键词: markov decision-processes

摘要

We study a certain polytope arising from embedding the Hamiltonian cycle problem in a discounted Markov decision process. The Hamiltonian cycle problem can be reduced to finding particular extreme points of a certain polytope associated with the input graph. This polytope is a subset of the space of discounted occupational measures. We characterize the feasible bases of the polytope for a general input graph G and determine the expected numbers of different types of feasible bases when the underlying graph is random. We utilize these results to demonstrate that augmenting certain additional constraints to reduce the polyhedral domain can eliminate a large number of feasible bases that do not correspond to Hamiltonian cycles. Finally, we develop a random walk algorithm on the feasible bases of the reduced polytope and present some numerical results. We conclude with a conjecture on the feasible bases of the reduced polytope.