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Editing Graphs Into Few Cliques: Complexity, Approximation, and Kernelization Schemes

  • Falk Hüffner
  • Christian Komusiewicz
  • André Nichterlein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9214)

Abstract

Given an undirected graph G and a positive integer k, the NP-hard Sparse Split Graph Editing problem asks to transform G into a graph that consists of a clique plus isolated vertices by performing at most k edge insertions and deletions; similarly, the \(P_3\)-Bag Editing problem asks to transform G into a graph which is the union of two possibly overlapping cliques. We give a simple linear-time 3-approximation algorithm for Sparse Split Graph Editing, an improvement over a more involved known factor-3.525 approximation. Further, we show that \(P_3\)-Bag Editing is NP-complete. Finally, we present a kernelization scheme for both problems and additionally for the 2-Cluster Editing problem. This scheme produces for each fixed \(\varepsilon \) in polynomial time a kernel of order \(\varepsilon k\). This is, to the best of our knowledge, the first example of a kernelization scheme that converges to a known lower bound.

Keywords

Degree Sequence Graph Class Graph Edit Split Graph Edge Deletion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Falk Hüffner
    • 1
  • Christian Komusiewicz
    • 1
  • André Nichterlein
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany

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