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Incremental maintenance of maximal cliques in a dynamic graph

  • Apurba DasEmail author
  • Michael Svendsen
  • Srikanta Tirthapura
Regular Paper
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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.

Keywords

Graph mining Maximal clique Incremental algorithm Dynamic graph 

Notes

Acknowledgements

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

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Iowa State UniversityAmesUSA

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