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Solving a “Hard” Problem to Approximate an “Easy” One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems

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Book cover Algorithm Engineering and Experimentation (ALENEX 2001)

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Abstract

We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields in near-linear time solutions as well as upper bounds. Using various computational tools, we get solutions within considerably less than 1% of the optimum.

An interesting feature of our approach is that, even though an FWP is hard to compute in theory and Edmonds’ algorithm for maximum weighted matching yields a polynomial solution for the MWMP, the practical behavior is just the opposite, and we can solve the FWP with high accuracy in order to find a good heuristic solution for the MWMP.

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Author information

Authors and Affiliations

  1. Department of Mathematics, TU Berlin, 10623, Berlin, Germany

    Sándor P. Fekete & Walter Tietze

  2. Department of Computing and Information Science, Queenś University, Kingston, Ontario, K7L 3N6, Canada

    Henk Meijer

  3. Forschungsinstitut für Diskrete Mathematik, Universität Bonn, 53113, Bonn, Germany

    André Rohe

Authors
  1. Sándor P. Fekete
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  2. Henk Meijer
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  3. André Rohe
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  4. Walter Tietze
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Editor information

Editors and Affiliations

  1. AT&T Labs Research, 180 Park Ave., P.O. Box 971, Florham Park, NJ, 07932-0000, USA

    Adam L. Buchsbaum

  2. Department of Computer Science, The University of North Carolina at Chapel Hill, CB 3175, Sitterson Hall, Chapel Hill, NC, 27599-3175, USA

    Jack Snoeyink

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© 2001 Springer-Verlag Berlin Heidelberg

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Fekete, S.P., Meijer, H., Rohe, A., Tietze, W. (2001). Solving a “Hard” Problem to Approximate an “Easy” One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems. In: Buchsbaum, A.L., Snoeyink, J. (eds) Algorithm Engineering and Experimentation. ALENEX 2001. Lecture Notes in Computer Science, vol 2153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44808-X_1

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  • DOI: https://doi.org/10.1007/3-540-44808-X_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42560-1

  • Online ISBN: 978-3-540-44808-2

  • eBook Packages: Springer Book Archive

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