Parallel Algorithms for Maximal Cliques in Circle Graphs and Unrestricted Depth Search
Universidade Federal de Mato Grosso do Sul,
Faculdade de Computação,
79070-900 Campo Grande, MS, Brazil; firstname.lastname@example.org
2 Universidade de São Paulo, Instituto de Matemática e Estatística, 05508-900 São Paulo, SP, Brazil; visiting professor of Universidade Federal do ABC; email@example.com
3 Universidade Federal do Rio de Janeiro, Instituto de Matemática, Núcleo de Computação Eletrônica and COPPE, 21.945-970 Rio de Janeiro, RJ, Brazil; firstname.lastname@example.org
Accepted: 2 June 2010
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.
Mathematics Subject Classification: 68W10 / 05C85 / 05C69
Key words: BSP/CGM algorithm / PRAM algorithm / circle graph / maximal clique / unrestricted depth search.
© EDP Sciences, 2010