A note on maximum independent sets and minimum clique partitions in unit disk graphs and penny graphs: complexity and approximation
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 3, pp. 331-346.

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.

DOI : 10.1051/ita/2011106
Classification : 05C69, 05C75, 68W25, 68Q25
Mots-clés : unit disk graphs, unit coin graphs, penny graphs, independent set, clique partition, approximation algorithms 
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     title = {A note on maximum independent sets and minimum clique partitions in unit disk graphs and penny graphs: complexity and approximation},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {331--346},
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Cerioli, Marcia R.; Faria, Luerbio; Ferreira, Talita O.; Protti, Fábio. A note on maximum independent sets and minimum clique partitions in unit disk graphs and penny graphs: complexity and approximation. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 3, pp. 331-346. doi : 10.1051/ita/2011106. http://www.numdam.org/articles/10.1051/ita/2011106/

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