Random Costs in Combinatorial Optimization
Disordered Systems and Neural Networks
2009-10-31 v3 Statistical Mechanics
Abstract
The random cost problem is the problem of finding the minimum in an exponentially long list of random numbers. By definition, this problem cannot be solved faster than by exhaustive search. It is shown that a classical NP-hard optimization problem, number partitioning, is essentially equivalent to the random cost problem. This explains the bad performance of heuristic approaches to the number partitioning problem and allows us to calculate the probability distributions of the optimum and sub-optimum costs.
Keywords
Cite
@article{arxiv.cond-mat/9907088,
title = {Random Costs in Combinatorial Optimization},
author = {Stephan Mertens},
journal= {arXiv preprint arXiv:cond-mat/9907088},
year = {2009}
}
Comments
4 pages, Revtex, 2 figures (eps), submitted to PRL