Efficiently computing k-edge connected components via graph decomposition

  • Authors:

  • Lijun Chang;Jeffrey Xu Yu;Lu Qin;Xuemin Lin;Chengfei Liu;Weifa Liang

  • Affiliations:

  • East China Normal University, University of New South Wales, Sydney, Australia;The Chinese University of Hong Kong, Hong Kong, China;The Chinese University of Hong Kong, Hong Kong, China;East China Normal University, University of New South Wales, Sydney, Australia;Swinburne University of Technology, Melbourne, Australia;Australian National University, Canberra, Australia

  • Venue:
  • Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
  • Year:
  • 2013

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Abstract

Efficiently computing k-edge connected components in a large graph, G = (V, E), where V is the vertex set and E is the edge set, is a long standing research problem. It is not only fundamental in graph analysis but also crucial in graph search optimization algorithms. Consider existing techniques for computing k-edge connected components are quite time consuming and are unlikely to be scalable for large scale graphs, in this paper we firstly propose a novel graph decomposition paradigm to iteratively decompose a graph G for computing its k-edge connected components such that the number of drilling-down iterations h is bounded by the "depth" of the k-edge connected components nested together to form G, where h usually is a small integer in practice. Secondly, we devise a novel, efficient threshold-based graph decomposition algorithm, with time complexity O(l × |E|), to decompose a graph G at each iteration, where l usually is a small integer with l « |V|. As a result, our algorithm for computing k-edge connected components significantly improves the time complexity of an existing state-of-the-art technique from O(|V|2|E| + |V|3 log |V|) to O(h × l × |E|). Finally, we conduct extensive performance studies on large real and synthetic graphs. The performance studies demonstrate that our techniques significantly outperform the state-of-the-art solution by several orders of magnitude.