Asymptotic analysis of an algorithm for balanced parallel processor scheduling
SIAM Journal on Computing
Statistical mechanics methods and phase transitions in optimizationproblems
Theoretical Computer Science - Phase transitions in combinatorial problems
Phase transition and finite-size scaling for the integer partitioning problem
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Poisson convergence in the restricted k-partitioning problem
Random Structures & Algorithms
Proof of the local REM conjecture for number partitioning. II. Growing energy scales
Random Structures & Algorithms
Proof of the local REM conjecture for number partitioning. II. Growing energy scales
Random Structures & Algorithms
Hi-index | 0.00 |
In this article we consider the number partitioning problem (NPP) in the following probabilistic version: Given n numbers X1,…,Xn drawn i.i.d. from some distribution, one is asked to find the partition into two subsets such that the sum of the numbers in one subset is as close as possible to the sum of the numbers in the other set. In this probabilistic version, the NPP is equivalent to a mean-field antiferromagnetic Ising spin glass, with spin configurations corresponding to partitions, and the energy of a spin configuration corresponding to the weight difference. Although the energy levels of this model are a priori highly correlated, a surprising recent conjecture of Bauke, Franz, and Mertens asserts that the energy spectrum of number partitioning is locally that of a random energy model (REM): the spacings between nearby energy levels are uncorrelated. More precisely, it was conjectured that the properly scaled energies converge to a Poisson process, and that the spin configurations corresponding to nearby energies are asymptotically uncorrelated. In this article, we prove these two claims, collectively known as the local REM conjecture. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009 This work was done while C.N. was a student at Stanford University and a post-doc at Microsoft Research.