Mining maximal cliques from a large graph using MapReduce: Tackling highly uneven subproblem sizes

2018 IEEE International Conference on Big Data (Big Data)

2018

Self Cite

Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasicliques from a graph is a robust way to detect densely connected structures with applications to bio-informatics and social network analysis. However, enumerating quasi-cliques in a graph is a challenging problem, even harder than the problem of enumerating cliques. We consider the enumeration of top-k degree-based quasi-cliques, and make the following contributions: (1) We show that even the problem of detecting if a given quasi-clique is maximal (i.e. not contained within another quasi-clique) is NPhard (2) We present a novel heuristic algorithm KERNELQC to enumerate the k largest quasi-cliques in a graph. Our method is based on identifying kernels of extremely dense subgraphs within a graph, following by growing subgraphs around these kernels, to arrive at quasi-cliques with the required densities (3) Experimental results show that our algorithm accurately enumerates quasi-cliques from a graph, is much faster than current state-of-the-art methods for quasi-clique enumeration (often more than three orders of magnitude faster), and can scale to larger graphs than current methods.

Section: Algorithm For Top-k Qcementioning

confidence: 99%

“…Much attention has been paid to the problem of enumerating cliques, which are complete dense structures in a graph, e.g. [1], [2], [3], [4], [5], [6]. Usually, however, dense subgraphs are not cliques.…”

Section: Introductionmentioning

confidence: 99%

Enumerating Top-k Quasi-Cliques

Sanei-Mehri

2018 IEEE International Conference on Big Data (Big Data)

2018

Self Cite

“…To compare with prior works in maximal clique enumeration, we implemented some of them [13], [14], [21], [18], [20] in Java, except the sequential algorithm GreedyBB [50], and the parallel algorithm Hashing [22], for which we used the executables provided by the authors (code written in C++). See Subsection V-D for more details.…”

Section: B Implementation Of the Algorithmsmentioning

confidence: 99%

Shared-Memory Parallel Maximal Clique Enumeration

Sanei-Mehri

2018 IEEE 25th International Conference on High Performance Computing (HiPC)

2018

Self Cite

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.

“…Other works on sequential algorithm for MBE on a static graph include [9], [10]. The authors of [26], [40], [36] present parallel algorithms for MBE and MCE for the MapReduce framework. Li et al [20] show a correspondence between closed itemsets in a transactional database and maximal bicliques in an appropriately defined graph.…”

Section: Related Workmentioning

confidence: 99%

Incremental Maintenance of Maximal Bicliques in a Dynamic Bipartite Graph

IEEE Trans. Multi-Scale Comp. Syst.

2018

Self Cite

We consider incremental maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition of edges. When new edges are added to the graph, we seek to enumerate the change in the set of maximal bicliques, without enumerating the set of maximal bicliques that remain unaffected. The challenge is to enumerate the change without explicitly enumerating the set of all maximal bicliques. In this work, we present (1)~Near-tight bounds on the magnitude of change in the set of maximal bicliques of a graph, due to a change in the edge set, and an (2)~Incremental algorithm for enumerating the change in the set of maximal bicliques. For the case when a constant number of edges are added to the graph, our algorithm is "change-sensitive", i.e., its time complexity is proportional to the magnitude of change in the set of maximal bicliques. To our knowledge, this is the first incremental algorithm for enumerating maximal bicliques in a dynamic graph, with a provable performance guarantee. Experimental results show that its performance exceeds that of baseline implementations by orders of magnitude. RightsPersonal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Abstract-We consider incremental maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition of edges. When new edges are added to the graph, we seek to enumerate the change in the set of maximal bicliques, without enumerating the set of maximal bicliques that remain unaffected. The challenge in an efficient algorithm is to enumerate the change without explicitly enumerating the set of all maximal bicliques. In this work, we present (1) Near-tight bounds on the magnitude of change in the set of maximal bicliques of a graph, due to a change in the edge set, and an (2) Incremental algorithm for enumerating the change in the set of maximal bicliques. For the case when a constant number of edges are added to the graph, our algorithm is "change-sensitive", i.e., its time complexity is proportional to the magnitude of change in the set of maximal bicliques. To our knowledge, this is the first incremental algorithm for enumerating maximal bicliques in a dynamic graph, with a provable performance guarantee. Our algorithm is easy to implement, and experimental results show that its performance exceeds that of baseline implementations by orders of magnitude.