A physicist's approach to number partitioning

Stephan Mertens

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arXiv · cond-mat/0009230

A physicist's approach to number partitioning

Stephan Mertens

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Abstract

The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase boundary that separates the ``easy-to-solve'' from the ``hard-to-solve'' phase of the NPP as well as for the probability distributions of the optimal and sub-optimal solutions. In addition, it can be shown that solving a number partioning problem of size $N$ to some extent corresponds to locating the minimum in an unsorted list of $\bigo{2^N}$ numbers. Considering this correspondence it is not surprising that known heuristics for the partitioning problem are not significantly better than simple random search.

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Stephan Mertens. 2000-11-23. A physicist's approach to number partitioning. https://arxiv.org/abs/cond-mat/0009230

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