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28 March 2024
 
  » arxiv » cond-mat/0009230

 Article overview


A physicist's approach to number partitioning
Stephan Mertens ;
Date 15 Sep 2000
Subject cond-mat
AffiliationOtto-von-Guericke Universität, Magdeburg
AbstractThe 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 $igo{2^N}$ numbers. Considering this correspondence it is not surprising that known heuristics for the partitioning problem are not significantly better than simple random search.
Source arXiv, cond-mat/0009230
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