A Multilevel Algorithm for the Minimum 2-sum Problem

In this paper we introduce a direct motivation for solving the minimum 2-sum problem, for which we present a linear-time algorithm inspired by the Algebraic Multigrid approach which is based on weighted edge contraction. Our results turned out to be better than previous results, while the short running time of the algorithm enabled experiments with very large graphs. We thus introduce a new benchmark for the minimum 2-sum problem which contains 66 graphs of various characteristics. In addition, we propose the straightforward use of a part of our algorithm as a powerful local reordering method for any other (than multilevel) framework. Article Type Communicated by Submitted Revised regular paper E. W. Mayr October 2004 Mar 2006 

• Type: Journal
• Year: 2006
• Where: JGAA
• Authors: Ilya Safro, Dorit Ron, Achi Brandt
• Keywords: Algebraic Multigrid Approach, Algorithm, JGAA 2006, Minimum 2-sum Problem