Shared-Memory Parallel Maximal Clique Enumeration

Abstract

We present shared-memory parallel methods for Maximal Clique Enumeration (MCE) from a graph. MCE is a fundamental and well-studied graph analytics task, and is a widely used primitive for identifying dense structures in a graph. Due to its computationally intensive nature, parallel methods are imperative for dealing with large graphs. However, surprisingly, there do not yet exist scalable and parallel methods for MCE on a shared-memory parallel machine. In this work, we present efficient 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 that they can scale to a large number of processors, and (3) our implementations on a multicore machine shows a good speedup and scaling behavior with increasing number of cores, and are substantially faster than prior shared-memory parallel algorithms for MCE.

Dynamic Maximal Cliques Detection and Evolution Management in Social Internet of Things: A Formal Concept Analysis Approach

“…Maximal cliques detection has been widely used in a set of fields, such as DNA detection and clique enumeration, and it can also tackle some critical problems of social networks. Das et al [32] utilized parallel graph algorithms to enumerate maximal cliques for further investigation of biological networks. Cheng et al [33] firstly proposed an efficient partition-based algorithm for MCE that addresses the problem of processing large graphs with limited memory.…”

Maximal clique enumeration problem on graphs: status and challenges

“…搜索算法, 具体细节会在第4节进行详细介绍. 广度优先搜索算法目前有Kose [39] 提出的一种从小团开 始不断合并的算法; 以及Yu [40] [43] 2014 Svendsen [44] 2010 Lu [45] 2010 Eppstein [42] 2010 Cheng [31] 2011 Cheng [46] 2017 Manoussakis [47] 2019 Manoussakis [48] 2012 Cheng [49] 2016 Conte [50] 2016 Chen [51] 2009 Schmidt [52] 2017 Lessley [53] 2018 Das [54] 2005 Zhang [55] 2014 Dasari [56] 2018 Segundo [57] 图 3 MCE计算优化工作的分类 Bron-Kerbosch [41] O(m) -unbounded O(n + q∆)…”

“…在筛选过程中, 其将枚举出的团 视为一个由顶点编号构成的字符串, 并利用字符串问题中的后缀树 [78] 来判断该团是否为重复的或非 极大的(由顶点序号组成的字符串在后缀树中是否有匹配项). 作者还在2019年提出了另一种筛选机 制 [48] , 对于一个在以v i 和其邻居中序号大于它的点作为点集的诱导子图中的极大团C, 如果原图中存 [49] 2017年, Lessley等人 [53] 用数据并行原语(DPPs)在共享内存、 多核架构下实现了Kose [39] Svendsen [44] Xu [71] Wu [43] Lessley [53] Das [54] Yu [40] Li [73] com- 2005年, Zhang等人 [55] 采用位向量的方式表示点的邻居和团的公共邻居, 优化了Kose [39] 算法的效 率, 但并没与解决内存需求的问题. 2014年, Dasari等人 [56] 用局部位邻接矩阵代替邻接表, 减小了工作集的大小, 提高数据局部性, 并且加速了集合的交集运算.…”

GraphMineSuite

“…Delivering theoretical performance bounds (facilitated by the GMS concurrency analysis). The BK in GMS offers the best work bound among poly-logarithmic depth maximal clique listing algorithms [42] and a recent algorithm by Eppstein et al [51] (GMS-DGR) using a novel performance metric "algorithmic throughput" that shows a number of maximal cliques found per second. Details of experimental setup: Section 8.…”