Random Costs in Combinatorial Optimization

Details Random Costs in Combinatorial Optimization Random Costs in Combinatorial Optimization

1999-07-06

arxiv.org/abs/cond-mat/9907088v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, Revtex, 2 figures (eps), submitted to PRL

Scientific paper

10.1103/PhysRevLett.84.1347

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.

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