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
Solving election manipulation using integer partitioning problems
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
A hybrid recursive multi-way number partitioning algorithm
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Heuristic algorithms for balanced multi-way number partitioning
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
The increasing cost tree search for optimal multi-agent pathfinding
Artificial 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 integers into a collection of subsets, so that the sum of the numbers in each subset are as nearly equal as possible. While a very efficient algorithm exists for optimal two-way partitioning, it is not nearly as effective for multi-way partitioning. We develop two new linear-space algorithms for multi-way partitioning, and demonstrate their performance on three, four, and five-way partitioning. In each case, our algorithms outperform the previous state of the art by orders of magnitude, in one case by over six orders of magnitude. Empirical analysis of the running times of our algorithms strongly suggest that their asymptotic growth is less than that of previous algorithms. The key insight behind both our new algorithms is that if an optimal k-way partition includes a particular subset, then optimally partitioning the numbers not in that set k-1 ways results in an optimal k-way partition.