Optimal Sequential Multi-Way Number Partitioning

Richard E. Korf, Ethan L. Schreiber, Michael D. Moffitt
2014 International Symposium on Artificial Intelligence and Mathematics  
Given a multiset of n positive integers, the NP-complete problem of number partitioning is to assign each integer to one of k subsets, such that the largest sum of the integers assigned to any subset is minimized. Last year, three different papers on optimally solving this problem appeared in the literature, two from the first two authors, and one from the third author. We resolve here competing claims of these papers, showing that different algorithms work best for different values of n and k,
more » ... with orders of magnitude differences in their performance. We combine the best ideas from both approaches into a new algorithm, called sequential number partitioning, and also introduce a hybrid algorithm that achieves the best performance for each value of n and k. Number partitioning is closely related to bin-packing, and advances in either problem can be applied to the other.
dblp:conf/isaim/KorfSM14 fatcat:fwgstyqztzdmldm3o7ohs42gqq