Abstract
We introduce the k-\(\mathcal{G}\)-Packing with t-Overlap problem to formalize the problem of finding communities in a network. In the k-\(\mathcal{G}\)-Packing with t-Overlap problem, we search for at least k communities with possible overlap. In contrast with previous work where communities are disjoint, we regulate the overlap through a parameter t. Our focus is the parameterized complexity of the k-\(\mathcal{G}\)-Packing with t-Overlap problem. Here, we provide a new technique for this problem generalizing the crown decomposition technique [2]. Using our global rule, we achieve a kernel with size bounded by 2(rk − r) for the k-\(\mathcal{G}\)-Packing with t-Overlap problem when t = r − 2 and \(\mathcal{G}\) is a clique of size r.
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Romero, J., López-Ortiz, A. (2014). The \({\mathcal{G}}\)-Packing with t-Overlap Problem. In: Pal, S.P., Sadakane, K. (eds) Algorithms and Computation. WALCOM 2014. Lecture Notes in Computer Science, vol 8344. Springer, Cham. https://doi.org/10.1007/978-3-319-04657-0_13
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DOI: https://doi.org/10.1007/978-3-319-04657-0_13
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