RAIRO-Theor. Inf. Appl.
Volume 45, Number 3, July-September 2011
|Page(s)||331 - 346|
|Published online||05 September 2011|
A note on maximum independent sets and minimum clique partitions in unit disk graphs and penny graphs: complexity and approximation
Instituto de Matemática and COPPE-Sistemas, Universidade Federal do Rio de Janeiro, Brazil. Partially supported by CNPq and FAPERJ. firstname.lastname@example.org
2 FFP, Universidade do Estado do Rio de Janeiro, Brazil. Partially supported by CNPq. email@example.com
3 COPPE-Sistemas, Universidade Federal do Rio de Janeiro, Brazil. Supported by CNPq. firstname.lastname@example.org
4 Instituto de Computação, Universidade Federal Fluminense, Brazil. Partially supported by CNPq and FAPERJ. email@example.com
Accepted: 23 March 2011
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.
Mathematics Subject Classification: 05C69 / 05C75 / 68W25 / 68Q25
Key words: Unit disk graphs / unit coin graphs / penny graphs / independent set / clique partition / approximation algorithms
© EDP Sciences, 2011
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