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A New Approach to Cactus Construction Applied to TSP Support Graphs

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Integer Programming and Combinatorial Optimization (IPCO 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2337))

Abstract

We present a novel approach to the construction of the cactus representation of all minimum cuts of a graph. The representation is a supergraph that stores the set of all mincuts compactly and mirrors its structure. We focus on support graphs occurring in the branch-and-cut approach to traveling salesman, vehicle routing and similar problems in a natural way. The ideas presented also apply to more general graphs. Unlike most previous construction approaches, we do not follow the Karzanov-Timofeev framework or a variation of it. Our deterministic algorithm is based on inclusion-minimal mincuts. We use Fleischer’s approach [J. Algorithms, 33(1):51–72, 1999], one of the fastest to date, as benchmark. The new algorithm shows an average speed-up factor of 20 for TSP-related support graphs in practice. We report computational results. Compared to the benchmark, we reduce the space required during construction for n-vertex graphs with m edges from to .

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Authors and Affiliations

  1. Institute of Computer Science, University of Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Klaus M. Wenger

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  1. Klaus M. Wenger
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Editors and Affiliations

  1. Program in Applied and Computational Mathematics, University of Princeton, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

    William J. Cook

  2. Sloan School of Management, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    Andreas S. Schulz

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Wenger, K.M. (2002). A New Approach to Cactus Construction Applied to TSP Support Graphs. In: Cook, W.J., Schulz, A.S. (eds) Integer Programming and Combinatorial Optimization. IPCO 2002. Lecture Notes in Computer Science, vol 2337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47867-1_9

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  • DOI: https://doi.org/10.1007/3-540-47867-1_9

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  • Print ISBN: 978-3-540-43676-8

  • Online ISBN: 978-3-540-47867-6

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