Efficient Multicore Algorithms For Identifying Biconnected Components

Abstract

In this paper we design and implement an algorithm for finding the biconnected components of a given graph. Our algorithm is based on experimental evidence that finding the bridges of a graph is usually easier and faster in the parallel setting. We use this property to first decompose the graph into independent and maximal 2-edge-connected subgraphs. To identify the articulation points in these 2-edge connected subgraphs, we again convert this into a problem of finding the bridges on an auxiliary graph.It is interesting to note that during the conversion process, the size of the graph may increase. However, we show that this small increase in size and the run time is offset by the consideration that finding bridges is easier in a parallel setting. We implement our algorithm on an Intel i7 980X CPU running 12 threads. We show that our algorithm is on average 2.45x faster than the best known current algorithms implemented on the same platform. Finally, we extend our approach to dense graphs by applying the sparsification technique suggested by Cong and Bader in [7].

Euler Meets GPU: Practical Graph Algorithms with Theoretical Guarantees

“…Follow-up works included heuristic improvements to the algorithm [15], and evaluation on the Explicit Multi-Threading (XMT) platform with promising results [19]. More recent papers [11,53] pointed out that Tarjan-Vishkin algorithm is not efficient on multi-core CPU. Instead, they suggested alternative heuristic solutions, without theoretical worst-case guarantees, based on breadth-first search and disregarding the Euler tour technique.…”

“…It involves multiple walks on the edges of the graph, and works particularly well for graphs with a small diameter. Implementations of the CK algorithm are state-of-the-art parallel biconnectivity algorithms for multi-core CPU [11] and GPU [61].…”

“…A tree edge is a bridge if and only if it never get marked. For a detailed description and a proof of correctness see [11,61].…”

“…A spanning tree algorithm for the first phase can be chosen arbitrarily, but a parallel BFS is used in most implementations [11,61]. The choice of BFS guarantees that the spanning tree depth is at most a factor of two from the minimum, which allows to bound the work performed in the marking phase by O(md), where d denotes the diameter.…”

“…The graphs are available for download from public repositories [3,17,36,46], and they commonly appear in experimental papers on biconnected components, e.g. [11,61], and GPU graph algorithms in general, e.g. [63].…”