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Statistical Mechanics Analysis of the Continuous Number Partitioning Problem

F. F. Ferreira·J. F. Fontanari
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Abstract

The number partitioning problem consists of partitioning a sequence of positive numbers ${a_1,a_2,..., a_N}$ into two disjoint sets, ${\cal A}$ and ${\cal B}$, such that the absolute value of the difference of the sums of $a_j$ over the two sets is minimized. We use statistical mechanics tools to study analytically the Linear Programming relaxation of this NP-complete integer programming. In particular, we calculate the probability distribution of the difference between the cardinalities of ${\cal A}$ and ${\cal B}$ and show that this difference is not self-averaging.

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BibTeXRIS

F. F. Ferreira, J. F. Fontanari. 1998-11-12. Statistical Mechanics Analysis of the Continuous Number Partitioning Problem. https://doi.org/10.1016/s0378-4371(99)00079-5

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