Leader election in plane cellular automata, only with left-right global convention

Authors:
Codrin Nichitiu;Christophe Papazian;Eric Rémila
Affiliations:
Equipe Universitaire de Recherche en Informatique de Saint-Etienne Universite St-Etienne, 23 rue Dr. Michelon, 42023 Saint-Etienne, France;Laboratoire de l'Informatique du Parallélisme, UMR 5668 CNRS-INRIA-ENS Lyon-Universite, Lyon 1 46 Allée d'Italie, 69364 Lyon Cedex 07, France;Laboratoire de l'Informatique du Parallélisme, UMR 5668 CNRS-INRIA-ENS Lyon-Universite, and Groupe de Recherche en Informatique et Mathématiques Appliquées, IUT Roanne (Universite S ...
Venue:
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Year:
2004

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Abstract

We give a linear time algorithm to elect a leader. This problem originated in networking and distributed computing research. Given a graph, its vertices represent processors (here finite state machines), and its edges communication lines (here synchronous). The leader election problem consists in finding a protocol for a family of graphs which, upon iteration, distinguishes a vertex, edge or cycle by a special state called leader. Here, the graphs are only required to be connected, and without holes. We describe the algorithm on a special class of planar graphs, prove its correctness and show how it extends to other classes.