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Statistical mechanics of combinatorial optimization problems with site disorder

Dean, David S. and Lancaster, David J. and Majumdar, Satya N. (2005) Statistical mechanics of combinatorial optimization problems with site disorder. Physical Review E, 72 (2). 026125. ISSN 1539-3755

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Official URL: http://link.aps.org/abstract/PRE/v72/e026125

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.

Item Type:Article
Additional Information:Online ISSN 1550-2376
Research Community:University of Westminster > Electronics and Computer Science, School of
ID Code:2197
Deposited On:27 Jun 2006
Last Modified:11 Aug 2010 15:30

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