Shared-memory Parallel Maximal Clique Enumeration from Static and Dynamic Graphs

Abstract

Maximal Clique Enumeration (MCE) is a fundamental graph mining problem, and is useful as a primitive in identifying dense structures in a graph. Due to the high computational cost of MCE, parallel methods are imperative for dealing with large graphs. We present shared-memory parallel algorithms for MCE, with the following properties: (1) the parallel algorithms are provably work-efficient relative to a state-of-the-art sequential algorithm (2) the algorithms have a provably small parallel depth, showing they can scale to a large number of processors, and (3) our implementations on a multicore machine show good speedup and scaling behavior with increasing number of cores, and are substantially faster than prior shared-memory parallel algorithms for MCE; for instance, on certain input graphs, while prior works either ran out of memory or did not complete in 5 hours, our implementation finished within a minute using 32 cores. We also present work-efficient parallel algorithms for maintaining the set of all maximal cliques in a dynamic graph that is changing through the addition of edges.

Unsupervised Fake News Detection

“…Across the three phases, GTUT uses various criteria and methods to progressively label all articles in A as shown in Figure 1. A tabular overview of the labelling progression and methods used appear in , as % of articles at the high and low end of the score spectrum respectively; 7 Phase 2; 8 Construct an article graph using edges weighted as in Eq. 8; 9 Learn article feature vectors using node2vec; 10 Use label spreading to label all articles within bi-cliques; 11 Phase 3; 12 Construct an article graph using edges weighted as in Eq.…”

“…Note on Scalability: While the bi-clique enumeration step, as may be obvious, would be the most computationally expensive step in GTUT, recent research in enumerating cliques have yielded massive scalability improvements. In particular, a recent method [8] reports clique enumeration methods that can complete in a matter of seconds over million-sized graphs. Our implementation, based on [44], yielded response times in the order of minutes over benchmark datasets we use in our empirical evaluation.…”

Maximal clique enumeration problem on graphs: status and challenges

“…k团问题 [22,23] 的定义为: 给定一个无向图, 找到所有包含k个 顶点的团. [30] 2010 Cheng [31] 2015 Xu [32] 2017 Sun [33] 2019 Das [34] 2020 Das [35] 2001 Kose [39] 2017 Yu [40] 2019 Yu [75] 1977 Tsukiyama [59] 2004 Makino [60] 2013 Chang [61] 2015 Comin [62] 2016 Conte [63] 1973 Bron [41] 2001 Koch [69] 2004 Tomita [58] 2006 Du [70] 2014 Xu [71] 2019 Li [73] On special graphs On general graphs 1965 Fulkerson [24] 1985 Chiba [27] 1992 Jerrum [28] 1993 Blair [29] 1995 Prisner [25] 2003 Spinrad [26] On uncertain graphs 2016 Mukherjee [36] 2019 Li [37] 图 2 MCE算法的分类 [36,37] . 在动态图上维护更新极大团枚举结果的工作由Stix在2004年首次提出 [30] , 对于图中的一条新增 边u → v, Stix对包含u的极大团和包含v的极大团进行笛卡尔积, 生成新图中所有可能存在的极大 团并一一验证.…”

Mining Maximal Clique Summary with Effective Sampling

“…Segundo et al [10] improved the practical performance of the algorithm by avoiding too much time consumed by selecting the pivot. With distributed computing paradigms, scalable and parallel algorithms were designed for MCE in [8], [9], [22], [23]. Schmidt et al [8] decomposed the search tree to enable parallelization.…”

“…Blanuša et al [22] developed a scalable parallel implementation by using hash-join-based set-intersection algorithms within MCE. Das et al [23] designed shared-memory parallel algorithms both for MCE and for maintaining the set of all maximal cliques on a dynamic graph. The I/O performance of MCE in massive networks was improved by [24], [25].…”