# Scaling and Universality in Continuous Length Combinatorial Optimization

@article{Aldous2003ScalingAU, title={Scaling and Universality in Continuous Length Combinatorial Optimization}, author={David Aldous and Allon G. Percus}, journal={Proceedings of the National Academy of Sciences of the United States of America}, year={2003}, volume={100 20}, pages={11211-5} }

- Published 2003 in Proceedings of the National Academy of Sciences…
DOI:10.1073/pnas.1635191100

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 delta2. For the minimum matching and traveling salesman problems in dimension d >/= 2, the increase scales as delta3; 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… CONTINUE READING

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