Asymptotic analysis of an algorithm for balanced parallel processor scheduling
SIAM Journal on Computing
Easily searched encodings for number partitioning
Journal of Optimization Theory and Applications
Exponentially small bounds on the expected optimum of the partition and subset sum problems
Random Structures & Algorithms
A complete anytime algorithm for number partitioning
Artificial Intelligence
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
The Differencing Method of Set Partitioning
The Differencing Method of Set Partitioning
From approximate to optimal solutions: a case study of number partitioning
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Statistical mechanics methods and phase transitions in optimizationproblems
Theoretical Computer Science - Phase transitions in combinatorial problems
Complexity of learning in artificial neural networks
Theoretical Computer Science - Phase transitions in combinatorial problems
Poisson convergence in the restricted k-partitioning problem
Random Structures & Algorithms
Is computational complexity a barrier to manipulation?
CLIMA'10 Proceedings of the 11th international conference on Computational logic in multi-agent systems
Is computational complexity a barrier to manipulation?
Annals of Mathematics and Artificial Intelligence
Where are the hard manipulation problems?
Journal of Artificial Intelligence Research
Finding well-balanced pairs of edge-disjoint trees in edge-weighted graphs
Discrete Optimization
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The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase boundary that separates the "easy-to-solve" from the "hard-to-solve" phase of the NPP as well as for the probability distributions of the optimal and sub-optimal solutions. In addition, it can be shown that solving a number portioning problem of size N to some extent corresponds to locating the minimum in an unsorted list of O(2N ) numbers. Considering this correspondence it is not surprising that known heuristics for the partitioning problem are not signi4cantly better than simple random search.