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A New Approach to Cactus Construction Applied to TSP Support Graphs

  • Klaus M. Wenger
Conference paper
Part of the Lecture Notes in Computer Science book series (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 Open image in new window to Open image in new window .

Keywords

Travel Salesman Problem Weighted Graph Tree Edge Capacitate Vehicle Route Problem Support Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Klaus M. Wenger
    • 1
  1. 1.Institute of Computer ScienceUniversity of HeidelbergHeidelbergGermany

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