The \({\mathcal{G}}\)-Packing with t-Overlap Problem

  • Jazmín Romero
  • Alejandro López-Ortiz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8344)


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.


Injective Function Overlap Problem Maximal Solution Reduction Rule Edge Disjoint 
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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jazmín Romero
    • 1
  • Alejandro López-Ortiz
    • 1
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooCanada

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