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}
}
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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