Statistical mechanics analysis of the continuous number partitioning problem

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 ai 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 shaw that this difference is not self-averaging. (C) 1999 Elsevier Science B.V. All rights reserved.