A physicist's approach to number partitioning

The statistical physics approach to the number partioning problem, a classical NPhard 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(2N ) numbers. Considering this correspondence it is not surprising that known heuristics for the partitioning problem are not significantly better than simple random search.