An exact combinatorial algorithm for minimum graph bisection

• 成果类型: Article
• 署名作者: Delling, Daniel; Fleischman, Daniel; Goldberg, Andrew V.; Razenshteyn, Ilya; Werneck, Renato F.
• 署名单位: Microsoft; Cornell University; Massachusetts Institute of Technology (MIT)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0811-z
• 发表日期: 2015
• 页码: 417-458
• 关键词: partitioning problem; optimization; image; planar

摘要

We present a novel exact algorithm for the minimum graph bisection problem, whose goal is to partition a graph into two equally-sized cells while minimizing the number of edges between them. Our algorithm is based on the branch-and-bound framework and, unlike most previous approaches, it is fully combinatorial. We introduce novel lower bounds based on packing trees, as well as a new decomposition technique that contracts entire regions of the graph while preserving optimality guarantees. Our algorithm works particularly well on graphs with relatively small minimum bisections, solving to optimality several large real-world instances (with up to millions of vertices) for the first time.