Distributed approximation algorithms for planar graphs

Authors:
Andrzej Czygrinow;Michał Hańćkowiak;Edyta Szymańska
Affiliations:
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ;Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland;Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
Venue:
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Year:
2006

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Abstract

In this paper we construct two distributed algorithms for computing approximations of a largest matching and a minimum dominating set in planar graphs on n vertices. The approximation ratio in both cases approaches one with n tending to infinity and the number of synchronous communication rounds is poly-logarithmic in n. Our algorithms are purely deterministic.