A linear time algorithm for the reverse 1-median problem on a cycle

  • Authors:

  • Rainer E. Burkard;Elisabeth Gassner;Johannes Hatzl

  • Affiliations:

  • Institute of Optimization and Discrete Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria;Institute of Optimization and Discrete Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria;Institute of Optimization and Discrete Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria

  • Venue:
  • Networks
  • Year:
  • 2006

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Abstract

This article deals with the reverse 1-median problem on graphs with positive vertex weights. The problem is proved to be strongly NP-hard even in the case of bipartite graphs and not approximable within a constant factor (unless P = NP). Furthermore, a linear time algorithm for the reverse 1-median problem on a cycle with linear cost functions (RMC) is developed. It is also shown that there exists an integral optimal solution of RMC if the input data are integral. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 48(1), 16-23 2006