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A note on maximum independent sets and minimum clique partitions in unit disk graphs and penny graphs: complexity and approximation

Published online by Cambridge University Press:  05 September 2011

Marcia R. Cerioli ,
Luerbio Faria ,
Talita O. Ferreira  and
Fábio Protti
Marcia R. Cerioli
Affiliation:
Instituto de Matemática and COPPE-Sistemas, Universidade Federal do Rio de Janeiro, Brazil. Partially supported by CNPq and FAPERJ. cerioli@cos.ufrj.br
Luerbio Faria
Affiliation:
FFP, Universidade do Estado do Rio de Janeiro, Brazil. Partially supported by CNPq. luerbio@cos.ufrj.br
Talita O. Ferreira
Affiliation:
COPPE-Sistemas, Universidade Federal do Rio de Janeiro, Brazil. Supported by CNPq. talita@cos.ufrj.br
Fábio Protti
Affiliation:
Instituto de Computação, Universidade Federal Fluminense, Brazil. Partially supported by CNPq and FAPERJ. fabio@ic.uff.br
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Abstract

A unit disk graph is the intersection graph of a family of unit disks in the plane. If the disks do not overlap, it is also a unit coin graph or penny graph. It is known that finding a maximum independent set in a unit disk graph is a NP-hard problem. In this work we extend this result to penny graphs. Furthermore, we prove that finding a minimum clique partition in a penny graph is also NP-hard, and present two linear-time approximation algorithms for the computation of clique partitions: a 3-approximation algorithm for unit disk graphs and a 2-approximation algorithm for penny graphs.

Keywords

Unit disk graphsunit coin graphspenny graphsindependent setclique partitionapproximation algorithms
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 45 , Issue 3 , July 2011 , pp. 331 - 346
Copyright
© EDP Sciences, 2011

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