Parallel algorithms for maximal cliques in circle graphs and unrestricted depth search
Cáceres, E. N. ; Song, S. W. ; Szwarcfiter, J. L.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010), p. 293-311 / Harvested from Numdam

We present parallel algorithms on the BSP/CGM model, with p processors, to count and generate all the maximal cliques of a circle graph with n vertices and m edges. To count the number of all the maximal cliques, without actually generating them, our algorithm requires O(log p) communication rounds with O(nm/p) local computation time. We also present an algorithm to generate the first maximal clique in O(log p) communication rounds with O(nm/p) local computation, and to generate each one of the subsequent maximal cliques this algorithm requires O(log p) communication rounds with O(m/p) local computation. The maximal cliques generation algorithm is based on generating all maximal paths in a directed acyclic graph, and we present an algorithm for this problem that uses O log (p) communication rounds with O(m/p) local computation for each maximal path. We also show that the presented algorithms can be extended to the CREW PRAM model.

Publié le : 2010-01-01
DOI : https://doi.org/10.1051/ita/2010016
Classification:  68W10,  05C85,  05C69
@article{ITA_2010__44_3_293_0,
     author = {C\'aceres, E. N. and Song, S. W. and Szwarcfiter, J. L.},
     title = {Parallel algorithms for maximal cliques in circle graphs and unrestricted depth search},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {44},
     year = {2010},
     pages = {293-311},
     doi = {10.1051/ita/2010016},
     mrnumber = {2761521},
     zbl = {pre05822254},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2010__44_3_293_0}
}
Cáceres, E. N.; Song, S. W.; Szwarcfiter, J. L. Parallel algorithms for maximal cliques in circle graphs and unrestricted depth search. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) pp. 293-311. doi : 10.1051/ita/2010016. http://gdmltest.u-ga.fr/item/ITA_2010__44_3_293_0/

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