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Approximation algorithms and hardness results for the clique packing problem
- Source :
-
Discrete Applied Mathematics . Apr2009, Vol. 157 Issue 7, p1396-1406. 11p. - Publication Year :
- 2009
-
Abstract
- Abstract: For a fixed family of graphs, an -packing in a graph is a set of pairwise vertex-disjoint subgraphs of , each isomorphic to an element of . Finding an -packing that maximizes the number of covered edges is a natural generalization of the maximum matching problem, which is just . In this paper we provide new approximation algorithms and hardness results for the -packing problem where . We show that already for the -packing problem is APX-complete, and, in fact, we show that it remains so even for graphs with maximum degree 4. On the positive side, we give an approximation algorithm with approximation ratio at most 2 for every fixed . For we obtain better approximations. For we obtain a simple -approximation, achieving a known ratio that follows from a more involved algorithm of Halldórsson. For , we obtain a -approximation, and for we obtain a -approximation. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 157
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 36969291
- Full Text :
- https://doi.org/10.1016/j.dam.2008.10.017