The statistical mechanics of multi-index matching problems with site disorder
David S. Dean, David Lancaster
TL;DR
This paper applies statistical mechanics to analyze multi-index matching problems with geometric site disorder, providing exact results at finite temperature and insights into optimal solutions and heuristics at zero temperature.
Contribution
It introduces a functional formalism to exactly analyze the thermodynamics of site-disordered matching problems, especially at zero temperature.
Findings
Exact average optimal match value at zero temperature
Insights into heuristic algorithms for maximal matching
Thermodynamic analysis of site disorder in matching problems
Abstract
We study the statistical mechanics of multi-index matching problems where the quenched disorder is a geometric site disorder rather than a link disorder. A recently developed functional formalism is exploited which yields exact results in the finite temperature thermodynamic limit. Particular attention is paid to the zero temperature limit of maximal matching problems where the method allows us to obtain the average value of the optimal match and also sheds light on the algorithmic heuristics leading to that optimal match
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