A complete anytime algorithm for number partitioning
Artificial Intelligence
Computing Partitions with Applications to the Knapsack Problem
Journal of the ACM (JACM)
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
Where are the really hard manipulation problems? the phase transition in manipulating the veto rule
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Search strategies for optimal multi-way number partitioning
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Improved bin completion for optimal bin packing and number partitioning
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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The number partitioning problem is to divide a given set of n positive integers into k subsets, so that the sum of the numbers in each subset are as nearly equal as possible. While effective algorithms for two-way partitioning exist, multiway partitioning is much more challenging. We introduce an improved algorithm for optimal multiway partitioning, by combining several existing algorithms with some new extensions. We test our algorithm for partitioning 31-bit integers from three to ten ways, and demonstrate orders of magnitude speedup over the previous state of the art.