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Incremental maintenance of maximal cliques in a dynamic graph

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Abstract

We consider the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges. We present nearly tight bounds on the magnitude of change in the set of maximal cliques when edges are added to the graph, as well as the first change-sensitive algorithm for incremental clique maintenance under edge additions, whose runtime is proportional to the magnitude of the change in the set of maximal cliques, when the number of edges added is small. Our algorithm can also be applied to the decremental case, when edges are deleted from the graph. We present experimental results showing these algorithms are efficient in practice and are faster than prior work by two to three orders of magnitude.

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  1. https://sites.google.com/site/murmurhash/.

  2. http://konect.uni-koblenz.de/.

  3. http://networkrepository.com/.

  4. https://sites.google.com/site/murmurhash/.

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Acknowledgements

AD and ST were supported in part by NSF Grants 1527541, 1725702, and 1632116.

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  1. Iowa State University, Ames, USA

    Apurba Das, Michael Svendsen & Srikanta Tirthapura

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  1. Apurba Das
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  2. Michael Svendsen
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  3. Srikanta Tirthapura
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Das, A., Svendsen, M. & Tirthapura, S. Incremental maintenance of maximal cliques in a dynamic graph. The VLDB Journal 28, 351–375 (2019). https://doi.org/10.1007/s00778-019-00540-5

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