IDEAS home Printed from https://ideas.repec.org/p/ems/eureir/22803.html
   My bibliography  Save this paper

Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/22803/EI2011-08.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ron Holzman, 1990. "An Axiomatic Approach to Location on Networks," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 553-563, August.
    2. Vohra, Rakesh, 1996. "An axiomatic characterization of some locations in trees," European Journal of Operational Research, Elsevier, vol. 90(1), pages 78-84, April.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mulder, H.M. & Novick, B., 2011. "A simple axiomatization of the median procedure on median graphs," Econometric Institute Research Papers EI2011-25, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. McMorris, F.R. & Novick, B. & Mulder, H.M. & Powers, R.C., 2015. "An ABC-Problem for Location and Consensus Functions on Graphs," Econometric Institute Research Papers EI 2015-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Changat, M. & Lekha, D.S. & Mulder, H.M. & Subhamathi, A.R., 2014. "Axiomatic Characterization of the Median and Antimedian Functions on Cocktail-Party Graphs and Complete Graphs," Econometric Institute Research Papers EI 2014-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. McMorris, F.R. & Mulder, H.M. & Novick, B. & Powers, R.C., 2014. "Five axioms for location functions on median graphs," Econometric Institute Research Papers EI 2014-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. 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.
    5. Mulder, H.M. & Novick, B., 2011. "A simple axiomatization of the median procedure on median graphs," Econometric Institute Research Papers EI2011-25, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. McMorris, F.R. & Mulder, Henry Martyn & Novick, Beth & Powers, Robert C., 2021. "Majority rule for profiles of arbitrary length, with an emphasis on the consistency axiom," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 164-174.
    7. Dean P. Foster & Rakesh V. Vohra, 1998. "An Axiomatic Characterization of a Class of Locations in Tree Networks," Operations Research, INFORMS, vol. 46(3), pages 347-354, June.
    8. Mulder, H.M. & Vohra, R.V., 2006. "Axiomatic characterization of the absolute median on cube-free median networks," Econometric Institute Research Papers EI 2006-26, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Masashi Umezawa, 2012. "The replacement principle for the provision of multiple public goods on tree networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 211-235, February.
    10. Herman Monsuur & Ton Storcken, 2004. "Centers in Connected Undirected Graphs: An Axiomatic Approach," Operations Research, INFORMS, vol. 52(1), pages 54-64, February.
    11. Changat, M. & Lekha, D.S. & Mohandas, S. & Mulder, H.M. & Subhamathi, A.R., 2015. "Axiomatic Characterization of the Median and Antimedian Function on a Complete Graph minus a Matching," Econometric Institute Research Papers EI2015-17, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Régis Renault & Alain Trannoy, 2011. "Assessing the extent of strategic manipulation: the average vote example," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 497-513, December.
    13. Righini, Giovanni, 1995. "A double annealing algorithm for discrete location/allocation problems," European Journal of Operational Research, Elsevier, vol. 86(3), pages 452-468, November.
    14. repec:dau:papers:123456789/12477 is not listed on IDEAS
    15. H. A. Eiselt & Vladimir Marianov, 2020. "Stability of utility functions and apportionment rules in location models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 772-792, October.
    16. Correa-Morris, Jyrko, 2021. "The median partition and submodularity," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    17. Noga Alon & Michal Feldman & Ariel D. Procaccia & Moshe Tennenholtz, 2010. "Strategyproof Approximation of the Minimax on Networks," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 513-526, August.
    18. Vohra, Rakesh V., 1999. "The replacement principle and tree structured preferences," Economics Letters, Elsevier, vol. 63(2), pages 175-180, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ems:eureir:22803. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: RePub (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.