Statistical mechanics of combinatorial optimization problems with site disorder

Dean, D.S., Lancaster, D.J. and Majumdar, S.N. 2005. Statistical mechanics of combinatorial optimization problems with site disorder. Physical Review E. 72 (2), p. 026125.

TitleStatistical mechanics of combinatorial optimization problems with site disorder
AuthorsDean, D.S., Lancaster, D.J. and Majumdar, S.N.
Abstract

We study the statistical mechanics of a class of problems whose phase space is the set of permutations of an ensemble of quenched random positions. Specific examples analyzed are the finite temperature traveling salesman problem on several different domains and various problems in one

dimension such as the so called descent problem. We first motivate our method by analyzing these problems using the annealed approximation, then the limit of a large number of points we develop a formalism to carry out the quenched calculation. This formalism does not require the replica

method and its predictions are found to agree with Monte Carlo simulations. In addition our method reproduces an exact mathematical result for the Maximum traveling salesman problem in two dimensions and suggests its generalization to higher dimensions. The general approach may provide an alternative method to study certain systems with quenched disorder.

JournalPhysical Review E
Journal citation72 (2), p. 026125
ISSN1539-3755
Year2005
FileDean_Lancaster_Majumdar_2005_final.pdf
Digital Object Identifier (DOI)doi:10.1103/PhysRevE.72.026125
Web address (URL)http://link.aps.org/abstract/PRE/v72/e026125
Publication dates
Published2005

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