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.
The first and the fourth authors were partly supported by the ANR grant BLAN06-1-138894 (projet OPTICOMB). The second and the third authors were supported by the ACI grant “Jeunes Chercheurs”(TAGADA project).
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Chepoi, V., Fevat, T., Godard, E., Vaxès, Y. (2007). A Self-stabilizing Algorithm for the Median Problem in Partial Rectangular Grids and Their Relatives. In: Prencipe, G., Zaks, S. (eds) Structural Information and Communication Complexity. SIROCCO 2007. Lecture Notes in Computer Science, vol 4474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72951-8_8
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