Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-01-31
Physics
Condensed Matter
Disordered Systems and Neural Networks
8+2 pages, 9 figures, PDF only
Scientific paper
10.1088/1742-5468/2004/04/P04003
Number partitioning is a classical problem from combinatorial optimisation. 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.
Bauke Heiko
Franz Silvio
Mertens Stephan
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