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Listing All Maximal Cliques in Large Sparse Real-World Graphs

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Experimental Algorithms (SEA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6630))

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Abstract

We implement a new algorithm for listing all maximal cliques in sparse graphs due to Eppstein, Löffler, and Strash (ISAAC 2010) and analyze its performance on a large corpus of real-world graphs. Our analysis shows that this algorithm is the first to offer a practical solution to listing all maximal cliques in large sparse graphs. All other theoretically-fast algorithms for sparse graphs have been shown to be significantly slower than the algorithm of Tomita et al. (Theoretical Computer Science, 2006) in practice. However, the algorithm of Tomita et al. uses an adjacency matrix, which requires too much space for large sparse graphs. Our new algorithm opens the door for fast analysis of large sparse graphs whose adjacency matrix will not fit into working memory.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of California, Irvine, USA

    David Eppstein & Darren Strash

Authors
  1. David Eppstein
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  2. Darren Strash
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Editors and Affiliations

  1. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  2. Division of Economics and Business, Colorado School of Mines, Engineering Hall 310, 816 15th Street, 80401, Golden, CO, USA

    Steffen Rebennack

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Eppstein, D., Strash, D. (2011). Listing All Maximal Cliques in Large Sparse Real-World Graphs. In: Pardalos, P.M., Rebennack, S. (eds) Experimental Algorithms. SEA 2011. Lecture Notes in Computer Science, vol 6630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20662-7_31

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  • DOI: https://doi.org/10.1007/978-3-642-20662-7_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20661-0

  • Online ISBN: 978-3-642-20662-7

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