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Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes

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  • Balakrishnan, K.
  • Changat, M.
  • Mulder, H.M.
  • Subhamathi, A.R.

Abstract

An antimedian of a profile $\\pi = (x_1, x_2, \\ldots , x_k)$ of vertices of a graph $G$ is a vertex maximizing the sum of the distances to the elements of the profile. The antimedian function is defined on the set of all profiles on $G$ and has as output the set of antimedians of a profile. It is a typical location function for finding a location for an obnoxious facility. The `converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for the two classes of graphs on which the antimedian is well-behaved: paths and hypercubes.

Suggested Citation

  • Balakrishnan, K. & Changat, M. & Mulder, H.M. & Subhamathi, A.R., 2011. "Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes," Econometric Institute Research Papers EI 2011-08, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:22803
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    References listed on IDEAS

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    1. Vohra, Rakesh, 1996. "An axiomatic characterization of some locations in trees," European Journal of Operational Research, Elsevier, vol. 90(1), pages 78-84, April.
    2. Ron Holzman, 1990. "An Axiomatic Approach to Location on Networks," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 553-563, August.
    3. McMorris, F.R. & Mulder, H.M. & Ortega, O., 2010. "Axiomatic Characterization of the Mean Function on Trees," Econometric Institute Research Papers EI 2010-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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    Cited by:

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