Abstract
Community search is the problem of finding a good community for a given set of query vertices. One of the most studied formulations of community search asks for a connected subgraph that contains all query vertices and maximizes the minimum degree. All existing approaches to min-degree-based community search suffer from limitations concerning efficiency, as they need to visit (large part of) the whole input graph, as well as accuracy, as they output communities quite large and not really cohesive. Moreover, some existing methods lack generality: they handle only single-vertex queries, find communities that are not optimal in terms of minimum degree, and/or require input parameters. In this work we advance the state of the art on community search by proposing a novel method that overcomes all these limitations: it is in general more efficient and effective—one/two orders of magnitude on average, it can handle multiple query vertices, it yields optimal communities, and it is parameter-free. These properties are confirmed by an extensive experimental analysis performed on various real-world graphs.
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To be precise, the GS algorithm runs in \(\mathcal {O}(m\times \alpha (n))\) time, where \(\alpha (\cdot )\) denotes the inverse Ackermann function.
In the implementation all levels corresponding to non-distinct cores can be omitted; thus, the actual number of levels of the tree is h.
Flickr is available at http://socialnetworks.mpi-sws.org/datasets, while all other graphs at https://snap.stanford.edu/data.
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Responsible editors: Joao Gama, Indre Zliobaite , Alipio Jorge, Concha Bielza.
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Barbieri, N., Bonchi, F., Galimberti, E. et al. Efficient and effective community search. Data Min Knowl Disc 29, 1406–1433 (2015). https://doi.org/10.1007/s10618-015-0422-1
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DOI: https://doi.org/10.1007/s10618-015-0422-1