A complete anytime algorithm for number partitioning

Richard E. Korf
1998 Artificial Intelligence  
Given a set of numbers, the two-way number 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. Based on a polynomial-time heuristic due to Karma&x and Karp, we present a new algorithm, called Complete Karmarkar-Karp (CKK), that optimally solves the general numberpartitioning problem, and significantly outperforms the best previously-known algorithms for large problem instances. For
more » ... bers with twelve significant digits or less, CKK can optimally solve twoway partitioning problems of arbitrary size in practice. For numbers with greater precision, CKK first returns the Karmarkx-Karp solution, then continues to find better solutions as time allows. Over seven orders of magnitude improvement in solution quality is obtained in less than an hour of running time. Rather than building a single solution one element at a time, or modifying a complete solution, CKK constructs subsolutions, and combines them together in all possible ways. This approach may be effective for other NP-hard problems as well. 0 1998 Elsevier Science B.V. All rights reserved.
doi:10.1016/s0004-3702(98)00086-1 fatcat:5bvt6n76nbf57mektzyo4cltfa