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unit disk graphs

RAIRO - Theoretical Informatics and Applications (1)

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A note on maximum independent sets and minimum clique partitions in unit disk graphs and penny graphs: complexity and approximation
Marcia R. Cerioli, Luerbio Faria, Talita O. Ferreira, Fábio Protti
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 45 / Issue 3 / July 2011

Published online by Cambridge University Press:

05 September 2011, pp. 331-346

Print publication:

July 2011
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A unit disk graph is the intersection graphof 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 setin 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 partitionin a penny graph is also NP-hard, and presenttwo linear-time approximation algorithms for the computation of clique partitions:a 3-approximation algorithm for unit disk graphsand a 2-approximation algorithm for penny graphs.