René van Bevern, Hannes Moser, and Rolf Niedermeier:

Kernelization Through Tidying: A Case Study Based on s-Plex Cluster Vertex Deletion.

In Proceedings of the 9th Latin American Theoretical Informatics Symposium (LATIN'10), Oaxaca, México, April 2010. Volume 6034 in Lecture Notes in Computer Science, pages 528–539, Springer-Verlag Berlin, Germany.

We introduce the NP-hard graph-based data clustering problem s-Plex Cluster Vertex Deletion, where the task is to delete at most k vertices from a graph so that the connected components of the resulting graph are s-plexes. In an s-plex, every vertex has an edge to all but at most s-1 other vertices; cliques are 1-plexes. We propose a new method for kernelizing a large class of vertex deletion problems and illustrate it by developing an O(k²s³)-vertex problem kernel for s-Plex Cluster Vertex Deletion that can be computed in O(ksn²) time, where n is the number of graph vertices. The corresponding "kernelization through tidying" exploits polynomial-time approximation results.

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@inproceedings{BMN10,
  author = {Ren{\'e} van Bevern and Hannes Moser
    and Rolf Niedermeier},
  title = {Kernelization Through Tidying---A Case Study Based on
    $s$-Plex Cluster Vertex Deletion},
  booktitle = {Proceedings of the 9th Latin American Theoretical
    Informatics Symposium (LATIN'10)},
  publisher = {Springer-Verlag Berlin, Germany},
  address = {Oaxaca, M{\'e}xico},
  year = {2010},
  series = {Lecture Notes in Computer Science},
  pages = {528--539},
  doi = {10.1007/978-3-642-12200-2_46},
  volume = {6034}
}