Maximal clique enumeration with data-parallel primitives

Abstract

The enumeration of all maximal cliques in an undirected graph is a fundamental problem arising in several research areas. We consider maximal clique enumeration on sharedmemory, multi-core architectures and introduce an approach consisting entirely of data-parallel operations, in an effort to achieve efficient and portable performance across different architectures. We study the performance of the algorithm via experiments varying over benchmark graphs and architectures. Overall, we observe that our algorithm achieves up to a 33-time speedup and 9-time speedup over state-of-theart distributed and serial algorithms, respectively, for graphs with higher ratios of maximal cliques to total cliques. Further, we attain additional speedups on a GPU architecture, demonstrating the portable performance of our data-parallel design.

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

“…For example, on the Wikipedia network with around 1.8 million vertices, 36.5 million edges, and 131.6 million maximal cliques, ParTTT achieves a 16.5x parallel speedup over the sequential algorithm, and the optimized ParMCE achieves a 21.5x speedup, and completed in approximately two minutes. In contrast, prior shared-memory parallel algorithms for MCE [16,34,65] failed to handle the input graphs that we considered, and either ran out of memory ( [34,65]) or did not complete in 5 hours ( [16]). On dynamic graphs, we observe that ParIMCE gives a 3x-19x speedup over a state-of-the-art sequential algorithm IMCE [13] on a multicore machine with 32 cores.…”

“…Du et al [15] present a output-sensitive shared-memory parallel algorithm for MCE, but their algorithm suffers from poor load balancing as also pointed out by Schmidt et al [51]. Lessley et al [34] present a shared memory parallel algorithm that generates maximal cliques using an iterative method, where in each iteration, cliques of size (k − 1) are extended to cliques of size k. The algorithm of [34] is memory-intensive,…”

DPP-PMRF: Rethinking Optimization for a Probabilistic Graphical Model Using Data-Parallel Primitives

“…While VTK-m's use as a vehicle for achieving platform portability and performance for visualization methods is becoming better understood, its use as the basis for platform portable analysis computations is largely unexplored. Recent work [23] uses a DPP formulation of a graph analytics problem, namely maximal clique enumeration (MCE). The results show that the DPP reformulation is competitive with a state-of-the-art implementation in locating maximal cliques, is platform portable with performance analysis on both CPU and GPU platforms, and offers significant evidence that this approach is viable for use on graph-based problems.…”

“…Thus, the ability to attain fine-grained concurrency and greater parallelism is limited by the non-parallel computations within each outer-parallel optimization task. Finally, for the construction of MRF neighborhoods, our new method makes use of a recent work on maximal clique enumeration using DPPs [23].…”

“…Our initialization procedure is similar to that of the reference PMRF, but differs in the following ways. First, all of our initialization operations and algorithms are designed in terms of DPP, exposing high levels of data-parallelism throughout the entire image segmentation pipeline; refer to [23] for the DPP-based enumeration of maximal cliques. Second, we represent G in a compressed, sparse row (CSR) format that fits compactly within shared memory; see [23] for details on the DPP construction of this graph.…”