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Clique counting is an important problem in a variety of network analytics applications. We provide an extensive literature review of subgraph enumeration, considering different problems associated to cliques, clique relaxations, and other kind of subgraphs. We then devise algorithms for the problems of enumerating k-cliques (i.e., complete subgraphs on k nodes) and one of their relaxations, called k-diamonds (i.e., cliques of size k with one missing edge). For the first problem we present simple and fast multicore parallel algorithms for counting the number of k-cliques in large undirected graphs, for any small constant k 4. Differently from existing solutions, which mainly target distributed memory settings (e.g., MapReduce), the proposed algorithms work on off-the-shelf shared-memory multicore platforms. For the second problem, we first devise a sequential algorithm for counting the number of k-diamonds in large undirected graphs, for any small constant k 4. A parallel extension of the sequential algorithm is then proposed, developing a MapReduce-based approach.

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Leon Garcia, Renan
Renan Leon Garcia is a Brazilian computer scientist with a degree in computer systems. He received a master´s degree in computer science in 2016. He was accepted by the EBW+ project (Euro-Brazilian Window Plus) in mid-2015 to study for a Ph.D. in Computer Science at the University of Rome La Sapienza. At the beginning of 2019 he completed his Ph.D.

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