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Scaling and Universality in Continuous Length Combinatorial Optimization

David Aldous·Allon G. Percus
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Abstract

We consider combinatorial optimization problems defined over random ensembles, and study how solution cost increases when the optimal solution undergoes a small perturbation delta. For the minimum spanning tree, the increase in cost scales as delta^2; for the mean-field and Euclidean minimum matching and traveling salesman problems in dimension d>=2, the increase scales as delta^3; this is observed in Monte Carlo simulations in d=2,3,4 and in theoretical analysis of a mean-field model. We speculate that the scaling exponent could serve to classify combinatorial optimization problems into a small number of distinct categories, similar to universality classes in statistical physics.

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David Aldous, Allon G. Percus. 2003-08-13. Scaling and Universality in Continuous Length Combinatorial Optimization. https://doi.org/10.1073/pnas.1635191100

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