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Computing median and antimedian sets in median graphs

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Abstract

The median (antimedian) set of a profile π=(u 1,…,u k ) of vertices of a graph G is the set of vertices x that minimize (maximize) the remoteness ∑ i d(x,u i ). Two algorithms for median graphs G of complexity O(n idim(G)) are designed, where n is the order and idim(G) the isometric dimension of G. The first algorithm computes median sets of profiles and will be in practice often faster than the other algorithm which in addition computes antimedian sets and remoteness functions and works in all partial cubes.

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Authors and Affiliations

  1. Department of Computer Applications, Cochin University of Science and Technology, Cochin 22, India

    Kannan Balakrishnan

  2. Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova 17, 2000, Maribor, Slovenia

    Boštjan Brešar

  3. Department of Futures Studies, University of Kerala, Trivandrum, 695034, India

    Manoj Changat & Ajitha R. Subhamathi

  4. Department of Mathematics and Computer Science, FNM, University of Maribor, Gosposvetska 84, 2000, Maribor, Slovenia

    Sandi Klavžar

  5. Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000, Ljubljana, Slovenia

    Matjaž Kovše

Authors
  1. Kannan Balakrishnan
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  2. Boštjan Brešar
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  3. Manoj Changat
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  4. Sandi Klavžar
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  5. Matjaž Kovše
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  6. Ajitha R. Subhamathi
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Corresponding author

Correspondence to Sandi Klavžar.

Additional information

Work supported by the Ministry of Science of Slovenia and by the Ministry of Science and Technology of India under the bilateral India-Slovenia grants BI-IN/06-07-002 and DST/INT/SLOV-P-03/05, respectively.

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Balakrishnan, K., Brešar, B., Changat, M. et al. Computing median and antimedian sets in median graphs. Algorithmica 57, 207–216 (2010). https://doi.org/10.1007/s00453-008-9200-4

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  • DOI: https://doi.org/10.1007/s00453-008-9200-4

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