Heiko Bauke et al J. Stat. Mech. (2004) P04003 doi:10.1088/1742-5468/2004/04/P04003
Heiko Bauke1, Silvio Franz2 and Stephan Mertens1
Show affiliationsNumber 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.
75.10.Nr Spin-glass and other random models
02.60.Pn Numerical optimization
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
Issue 04 (April 2004)
Received 27 January 2004, accepted for publication 31 March 2004
Published 19 April 2004
Heiko Bauke et al J. Stat. Mech. (2004) P04003
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