Abstract
In this paper, we are concerned with the notion of k-plex, a relaxation model of clique, where degree of relaxation is controlled by the parameter k. Particularly, we present an efficient algorithm for detecting a maximum k-plex in a given simple undirected graph. Existing algorithms for extracting a maximum k-plex do not work well for larger k-values because the number of k-plexes exponentially grows as k becomes larger. In order to design an efficient algorithm for the problem, we introduce a notion of properness of k-plex. Our algorithm tries to iteratively find a maximum proper ℓ-plex, decreasing the value of ℓ from k to 1. At each iteration stage, the maximum size of proper ℓ-plex found so far can work as an effective lower bound which makes our branch-and-bound pruning more powerful. Our experimental results for several benchmark graphs show that our algorithm can detect maximum k-plexes much faster than SPLEX, the existing most efficient algorithm.
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Okubo, Y., Matsudaira, M., Haraguchi, M. (2014). Detecting Maximum k-Plex with Iterative Proper ℓ-Plex Search. In: Džeroski, S., Panov, P., Kocev, D., Todorovski, L. (eds) Discovery Science. DS 2014. Lecture Notes in Computer Science(), vol 8777. Springer, Cham. https://doi.org/10.1007/978-3-319-11812-3_21
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DOI: https://doi.org/10.1007/978-3-319-11812-3_21
Publisher Name: Springer, Cham
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