A physicist's approach to number partitioning

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 O(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. (C) 2001 Elsevier Science B.V. All rights reserved.