Number partitioning as a random energy model
Heiko Bauke, Silvio Franz, Stephan Mertens · Journal of Statistical Mechanics Theory and Experiment · 2004
Number partitioning is a classical problem from combinatorial optimization. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number partitioning behave like uncorrelated random variables. We claim that neighbouring energy levels are uncorrelated almost everywhere on the energy axis, and that energetically adjacent configurations are uncorrelated, too. Apparently there is no relation between geometry (configuration) and energy that could be exploited by an optimization algorithm. This ‘local random energy’ picture of number partitioning is corroborated by numerical simulations and heuristic arguments.