A self-stabilizing algorithm for the median problem in partial rectangular grids and their relatives

Authors:
Victor Chepoi;Tristan Fevat;Emmanuel Godard;Yann Vaxès
Affiliations:
Laboratoire d'Informatique Fondamentale de Marseille, UMR, Marseille, France;Laboratoire d'Informatique Fondamentale de Marseille, UMR, Marseille, France;Laboratoire d'Informatique Fondamentale de Marseille, UMR, Marseille, France;Laboratoire d'Informatique Fondamentale de Marseille, UMR, Marseille, France
Venue:
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Year:
2007

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Abstract

Given a graph G = (V, E), a vertex v of G is a median vertex if it minimizes the sum of the distances to all other vertices of G. The median problem consists in finding the set of all median vertices of G. In this note, we present a self-stabilizing algorithm for the median problem in partial rectangular grids. Our algorithm is based on the fact that partial rectangular grids can be isometrically embedded into the Cartesian product of two trees, to which we apply the algorithm proposed by Antonoiu, Srimani (1999) and Bruell, Ghosh, Karaata, Pemmaraju (1999) for computing the medians in trees. Then we extend our approach from partial rectangular grids to plane quadrangulations.