A complete anytime algorithm for number partitioning
Artificial Intelligence
Partitioning and Scheduling Parallel Programs for Multiprocessors
Partitioning and Scheduling Parallel Programs for Multiprocessors
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
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
An improved algorithm for optimal bin packing
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Tractable Pareto optimization of temporal preferences
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Temporal constraint reasoning with preferences
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Bin-completion algorithms for multicontainer packing and covering problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Where are the hard manipulation problems?
Journal of Artificial Intelligence Research
A hybrid recursive multi-way number partitioning algorithm
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Bounded suboptimal search: a direct approach using inadmissible estimates
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Comparing solution methods for the machine reassignment problem
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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The number partitioning problem seeks to divide a set of n numbers across k distinct subsets so as to minimize the sum of the largest partition. In this work, we develop a new optimal algorithm for multi-way number partitioning. A critical observation motivating our methodology is that a globally optimal k-way partition may be recursively constructed by obtaining suboptimal solutions to subproblems of size k - 1. We introduce a new principle of optimality that provides necessary and sufficient conditions for this construction, and use it to strengthen the relationship between sequential decompositions by enforcing upper and lower bounds on intermediate solutions. We also demonstrate how to further prune unpromising partial assignments by detecting and eliminating dominated solutions. Our approach outperforms the previous state-of-the-art by up to four orders of magnitude, reducing average runtime on the largest benchmarks from several hours to less than a second.