Minimum clique partition in unit disk graphs

The minimum clique partition (MCP) problem is that of partitioning the vertex set of a given graph into a minimum number of cliques. Given n points in the plane, the corresponding unit disk graph (UDG) has these points as vertices, and edges connecting points at distance at most 1. MCP in UDGs is known to be NP-hard and several constant factor approximations are known, including a recent PTAS. We present two improved approximation algorithms for MCP in UDGs with a realization: (I) A polynomial time approximation scheme (PTAS) running in time n(Omicron(1/epsilon 2)). This improves on a previous PTAS with n(Omicron(1/epsilon 4)) running time by Pirwani and Salavatipour (arXiv:0904.2203v1, 2009). (II) A randomized quadratic-time algorithm with approximation ratio 2.16. This improves on a ratio 3 algorithm with O(n (2)) running time by Cerioli et al. (Electron. Notes Discret. Math. 18:73-79, 2004).


Published in:
Graphs and Combinatorics , 27, 399-411
Year:
2011
Publisher:
Springer Verlag
ISSN:
0911-0119
Keywords:
Laboratories:




 Record created 2011-12-12, last modified 2018-03-17


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