Title: Algorithms for the remoteness function, and the median and antimedian sets in ℓ₁-graphs

Authors: Manoj Changat; Divya Sindhu Lekha; Ajitha R. Subhamathi

Addresses: Department of Futures Studies, University of Kerala, Trivandrum – 695 034, India ' Department of Information Technology, College of Engineering and Management Punnapra, Alappuzha – 688 003, India ' Department of Computer Applications, N.S.S. College Rajakumari, Idukki, Kerala, India

Abstract: The median (antimedian) set of a profile of vertices of a graph G is the set of vertices that minimise (maximise) the remoteness value. The median and antimedian problem of profiles on graphs is one of the basic models of desirable (as well as obnoxious) facility location problem in networks. The medians and antimedians behave nicely in classes of graphs like complete graphs, hypercubes and paths. In this paper, we study more classes of graphs in which the medians and antimedians have a nice structure, which admit a scale-embedding into hypercubes known as ℓ₁-graphs and design algorithms for both (median and antimedian) problems. We particularly discuss the cases of half-cubes, Johnson graphs and cocktail-party graphs.

Keywords: l1-graphs; remoteness function; median sets; antimedian sets; vertices; facility location; networks; hypercubes; half-cubes; Johnson graphs; cocktail-party graphs; finite connected graphs.

DOI: 10.1504/IJCSM.2015.072962

International Journal of Computing Science and Mathematics, 2015 Vol.6 No.5, pp.480 - 491

Received: 23 Jul 2013
Accepted: 24 Mar 2014
Published online: 10 Nov 2015 *

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