On computing all maximal cliques distributedly

Protti, Fábio; França, Felipe M. G.; Szwarcfiter, Jayme Luiz

doi:10.1007/3-540-63138-0_4

Cited by 6 publications

(3 citation statements)

References 10 publications

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“…Klein [21], Naor et al [25], Ho and Lee [18] present parallel algorithms for this problem for Chordal Graphs. Distributed algorithms for this problem are presented by Jennings and Motyckova [19] for network graphs and by Protti et al [26] for general graphs. An approximation algorithm is presented by Gupta et al [17] for unit disk graphs.…”

Section: Motivation and Previous Workmentioning

confidence: 99%

Parallel Algorithms for Maximal Cliques in Circle Graphs and Unrestricted Depth Search

Cáceres

Song

Szwarcfiter

2010

RAIRO-Theor. Inf. Appl.

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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.

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Section: Motivation and Previous Workmentioning

confidence: 99%

Parallel Algorithms for Maximal Cliques in Circle Graphs and Unrestricted Depth Search

Cáceres

Song

Szwarcfiter

2010

RAIRO-Theor. Inf. Appl.

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“…It was developed for sociological applications and has many extensions [4]. F. Protti et al developed a distributed algorithm to compute all maximal cliques [5], and B. Wu et al realized their theoretical distributed method in MapReduce computing model and effectively utilized its execution mechanism [6].…”

Section: Introductionmentioning

confidence: 99%

Mining Web Browsing Log by Using Relaxed Biclique Enumeration Algorithm in MapReduce

Su¹,

Tsao²,

Chu³

et al. 2012

2012 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology

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We propose a novel data mining framework using relaxed biclique for heterogeneous data. The framework is composed of three algorithms. First, an enumeration algorithm transforms heterogeneous databases into relaxed bicliques. Second, a tracking algorithm is used to find the biclique's variations over time. Finally, a ranking algorithm classifies relaxed bicliques into groups according to their statistical properties and dynamic behaviors. The framework is highly flexible and can be easily extended to applications in different domains. The framework is implemented in MapReduce and is proven to be scalable for processing large-scale data in a reasonable amount of time. In addition, the experiments show that the algorithms are both scalable and efficient. The proposed framework can also be applied to web network analysis and deliver rapid-response solutions.

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“…The problem of deciding whether a graph G is a clique‐inverse graph of

F_{p}

, when p is a constant, can be solved in polynomial time [13]. This can be easily seen by observing that if

G \in K^{- 1} ({MJX-tex-caligraphicscriptF}_{p})

then each vertex of G is in at most p − 1 maximal cliques, that is, G contains at most ( p − 1) n maximal cliques; then, K ( G ) can be determined in polynomial time by using any polynomial‐delay algorithm for the generation of the maximal cliques of a graph, for example [11]. In addition, checking whether the clique number of K ( G ) is at most p − 1 amounts to analyzing all the