Journal ArticleDOI
Hamiltonian Cycles and Markov Chains
Jerzy A. Filar,Dmitry Krass +1 more
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New characterizations of the Hamiltonian cycles of a directed graph, and a new LP-relaxation of the Traveling Salesman Problem are derived via an embedding of these combinatorial optimization problems in suitably perturbed controlled Markov chains.Abstract:
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 embedding of these combinatorial optimization problems in suitably perturbed controlled Markov chains. This embedding lends probabilistic interpretation to many of the quantities of interest, which in turn lead naturally to the introduction of a quadratic entropy-like function.read more
Citations
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Journal ArticleDOI
Constrained Discounted Markov Decision Processes and Hamiltonian Cycles
TL;DR: The Hamiltonian Cycle Problem is a special case of each of the following three problems for discrete time Markov Decision Processes with finite states and action sets and is shown to be NP-hard.
Proceedings Article
Stationary deterministic policies for constrained MDPs with multiple rewards, costs, and discount factors
TL;DR: In this paper, the problem of policy optimization for a resource-limited agent with multiple time-dependent objectives, represented as an MDP with multiple discount factors in the objective function and constraints, is considered.
Book ChapterDOI
Singular Perturbations of Markov Chains and Decision Processes
TL;DR: In this article, a unified treatment of both singular and regular perturbations in finite Markov chains and decision processes is presented, based on the analysis of series expansions of various important entities such as the perturbed stationary distribution matrix, the deviation matrix, and the mean-passage times matrix.
Journal ArticleDOI
Locating Discretionary Service Facilities Based on Probabilistic Customer Flows
TL;DR: It is shown that by employing the theory of constrained Markov Decision Processes this problem can be reformulated as a linear Mixed Integer Program.
Journal ArticleDOI
An Interior Point Heuristic for the Hamiltonian Cycle Problem via Markov Decision Processes
TL;DR: An interior-point type algorithm that involves an arc elimination heuristic that appears to perform rather well in moderate size graphs is developed, and can be approximated by quadratic functions that are almost convex and suitable for the application of logarithmic barrier methods.
References
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Journal ArticleDOI
Combinatorial optimization: algorithms and complexity
TL;DR: This clearly written, mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NPcomplete problems, more.
The traveling salesman problem
TL;DR: This study tested human performance on a real and virtual floor, as well as in a threedimensional (3D) virtual space, and modeled these results by a graph pyramid algorithm, which suggests that deterioration of performance in the 3D space can be attributed to geometrical relations between hierarchical clustering in a3D space and coarse-to-fine production of a tour.
Book
The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization
TL;DR: In this paper, Johnson and Papadimitriou proposed a performance guarantee for heuristics, based on the notion of well-solved special cases (P. Gilmore, et al.).
Book
Linear programming and finite Markovian control problems
TL;DR: This text is a revised version of the author's thesis for the University of Leiden and is mainly concerned with the theory of finite Markov decision problems.