pbitMCE: A bit-based approach for maximal clique enumeration on multicore processors

Abstract

Maximal clique enumeration (MCE) is a fundamental problem in graph theory. It plays a vital role in many network analysis applications and in computational biology. MCE is an extensively studied problem. Recently, Eppstein et al. proposed a state-of-the-art sequential algorithm that uses degeneracy based ordering of vertices to improve the efficiency. In this paper, we propose a new parallel implementation of the algorithm of Eppstein et al. using a new bit-based data structure. The new data structure not only reduces the working set size significantly but also by enabling the use of bit-parallelism improves the performance of the algorithm. We illustrate the significance of degeneracy ordering in load balancing and experimentally evaluate the impact of scheduling on the performance of the algorithm. We present experimental results on several types of synthetic and real-world graphs with up to 50 million vertices and 100 million edges. We show that our approach outperforms Eppstein et al.'s approach by up to 4 times and also scales up to 29 times when run on a multicore machine with 32 cores.Index Terms-maximal clique, bit-parallel, multicore, degeneracy, parallel algorithm.978-1-4799-7615-7/14/$31.00 ©2014 IEEE

A Method for Solving Graph Np-Complete Tasks on Reconfigurable Computer Systems Based on the Iteration Parallelizing Principle

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Efficiently enumerating all maximal cliques with bit-parallelism

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“…For graphs with low degeneracy, their technique rivals the speed of standard pivoting algorithms, while consuming only O(n + m) space. Additionally, their algorithm can be further sped up with bit-parallelism using the strategy of Dasari et al [20], giving consistent speed gains of 2-4x.…”

“…For sparse graphs, the algorithm by Eppstein et al [8] rivals that of Tomita et al [7] while only consuming space linear in the size of the graph, whereas the algorithm of Tomita et al requires quadratic space to store an adjacency matrix. Dasari et al [20] further improved this result by factors of 2-4x using bit-parallelism, though the main algorithm remains unchanged. For larger instances, external memory algorithms have been developed which take advantage of the property that real-world sparse graphs typically have small induced subgraphs that can fit into memory [21].…”