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A linear algorithm for the pos/neg-weighted 1-median problem on a cactus

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Abstract

The 1-median problem on a network asks for a vertex minimizing the sum of the weighted shortest path distances from itself to all other vertices, each associated with a certain positive weight. We allow fornegative weights as well and devise an exact algorithm for the resulting ‘pos/neg-weighted’ problem defined on a cactus. The algorithm visits every vertex just once and runs thus in linear time.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010, Graz, Austria

    R. E. Burkard

  2. Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100, Copenhagen, Denmark

    J. Krarup

Authors
  1. R. E. Burkard
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  2. J. Krarup
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Additional information

This research has been supported by the Spezialforschungsbereich F 003 ‘Optimierung und Kontrolle’, Projektbereich Diskrete Optimierung.

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Burkard, R.E., Krarup, J. A linear algorithm for the pos/neg-weighted 1-median problem on a cactus. Computing 60, 193–215 (1998). https://doi.org/10.1007/BF02684332

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  • DOI: https://doi.org/10.1007/BF02684332

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