Abstract
The number partitioning problem consists of partitioning a sequence of positive numbers { a 1, a 2,…, a N } into two disjoint sets, A and 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 A and B and show that this difference is not self-averaging.
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