Average parameterization and partial kernelization for computing medians

  • Authors:

  • Nadja Betzler;Jiong Guo;Christian Komusiewicz;Rolf Niedermeier

  • Affiliations:

  • Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany;Universität des Saarlandes, Campus E 1.4, D-66123 Saarbrücken, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2011

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Abstract

We propose an effective polynomial-time preprocessing strategy for intractable median problems. Developing a new methodological framework, we show that if the input objects of generally intractable problems exhibit a sufficiently high degree of similarity between each other on average, then there are efficient exact solving algorithms. In other words, we show that the median problems Swap Median Permutation, Consensus Clustering, Kemeny Score, and Kemeny Tie Score all are fixed-parameter tractable with respect to the parameter ''average distance between input objects''. To this end, we develop the novel concept of ''partial kernelization'' and, furthermore, identify polynomial-time solvable special cases for the considered problems.