Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The constrainedness knife-edge
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A physicist's approach to number partitioning
Theoretical Computer Science - Phase transitions in combinatorial problems
Two-dimensional packing algorithms for layout of disconnected graphs
Information Sciences—Informatics and Computer Science: An International Journal
From approximate to optimal solutions: constructing pruning and propagation rules
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Switching from bidirectional to unidirectional search
IJCAI'99 Proceedings of the 16th international joint conference on Artificial intelligence - Volume 2
Incomplete tree search using adaptive probing
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Backbones in optimization and approximation
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Algorithms for memory hierarchies: advanced lectures
Algorithms for memory hierarchies: advanced lectures
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Improved limited discrepancy search
AAAI'96 Proceedings of the thirteenth national 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
Where are the hard manipulation problems?
Journal of Artificial Intelligence Research
Fast loop-level data dependence profiling
Proceedings of the 26th ACM international conference on Supercomputing
Search strategies for optimal multi-way number partitioning
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Annals of Mathematics and Artificial Intelligence
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Given a set of numbers, the two-way partitioning problem is to divide them into two subsets, so that the sum of the numbers in each subset are as nearly equal as possible. The problem is NP-complete, and is contained in many scheduling applications. Based on a polynomial-time heuristic due to Karmarkar and Karp, we present a new algorithm, called Complete Karmarkar Karp (CKK), that optimally solves the general number-partitioning problem. CKK significantly outperforms the best previously-known algorithms for this problem. By restricting the numbers to twelve significant digits, we can optimally solve two-way partitioning problems of arbitrary size in practice. CKK first returns the Karmarkar-Karp solution, then continues to find better solutions as time allows. Almost five orders of magnitude improvement in solution quality is obtained within a minute of running time. Rather than building a single solution one element at a time, CKK constructs subsolutions, and combines them in all possible ways. CKK is directly applicable to the 0/1 knapsack problem, since it can be reduced to number partitioning. This general approach may also be applicable to other NP-hard problems as well.