An exact combinatorial algorithm for minimum graph bisection
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Author(s)
Delling, Daniel
Fleischman, Daniel
Goldberg, Andrew V.
Razenshteyn, Ilya
Werneck, Renato F.
Date Issued
September 2014
Journal
Mathematical Programming
Publisher
Springer Berlin Heidelberg
Citation
Delling, Daniel, Daniel Fleischman, Andrew V. Goldberg, Ilya Razenshteyn, and Renato F. Werneck. “An Exact Combinatorial Algorithm for Minimum Graph Bisection.” Math. Program. 153, no. 2 (September 10, 2014): 417–458.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10107-014-0811-z
