JSTAT (2004) P04003 ournal of Statistical Mechanics: An IOP and SISSA journal J Theory and Experiment Number partitioning as a random energy model Heiko Bauke 1 , Silvio Franz 2 and Stephan Mertens 1 1 Institut f¨ ur Theoretische Physik, Otto-von-Guericke Universit¨ at, PF 4120, 39016 Magdeburg, Germany 2 The Abdus Salam International Centre for Theoretical Physics, Condensed Matter Section, Strada Costiera 11, 34014 Trieste, Italy E-mail: heiko.bauke@physik.uni-magdeburg.de, franz@ictp.trieste.it and stephan.mertens@physik.uni-magdeburg.de Received 27 January 2004 Accepted 31 March 2004 Published 19 April 2004 Online at stacks.iop.org/JSTAT/2004/P04003 DOI: 10.1088/1742-5468/2004/04/P04003 Abstract. 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. Keywords: disordered systems (theory), energy landscapes (theory), heuristics c 2004 IOP Publishing Ltd PII: S1742-5468(04)78491-5 1742-5468/04/P04003+15$30.00