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Parameterized Dynamic Cluster Editing

Authors Junjie Luo, Hendrik Molter, André Nichterlein, Rolf Niedermeier

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Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • graph-based data clustering
  • goal-oriented clustering
  • compromise clustering
  • NP-hard problems
  • fixed-parameter tractability
  • parameterized hardness

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Abstract

We introduce a dynamic version of the NP-hard Cluster Editing problem. The essential point here is to take into account dynamically evolving input graphs: Having a cluster graph (that is, a disjoint union of cliques) that represents a solution for a first input graph, can we cost-efficiently transform it into a "similar" cluster graph that is a solution for a second ("subsequent") input graph? This model is motivated by several application scenarios, including incremental clustering, the search for compromise clusterings, or also local search in graph-based data clustering. We thoroughly study six problem variants (edge editing, edge deletion, edge insertion; each combined with two distance measures between cluster graphs). We obtain both fixed-parameter tractability as well as parameterized hardness results, thus (except for two open questions) providing a fairly complete picture of the parameterized computational complexity landscape under the perhaps two most natural parameterizations: the distance of the new "similar" cluster graph to (i) the second input graph and to (ii) the input cluster graph.

Cite As Get BibTex

Junjie Luo, Hendrik Molter, André Nichterlein, and Rolf Niedermeier. Parameterized Dynamic Cluster Editing. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 46:1-46:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.FSTTCS.2018.46

Author Details

Junjie Luo
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Berlin, Germany, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China , School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China
Hendrik Molter
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Berlin, Germany
André Nichterlein
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Berlin, Germany
Rolf Niedermeier
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Berlin, Germany

Funding

  • Luo, Junjie: Supported by CAS-DAAD Joint Fellowship Program for Doctoral Students of UCAS. Work done while with TU Berlin.
  • Molter, Hendrik: Supported by the DFG, project MATE (NI 369/17).

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