Parameterized Dynamic Cluster Editing

Junjie Luo, Hendrik Molter, André Nichterlein, Rolf Niedermeier

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We introduce a dynamic version of the NP-hard graph modification problem Cluster Editing. The essential point here is to take into account dynamically evolving input graphs: having a cluster graph (that is, a disjoint union of cliques) constituting 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 (three modification scenarios 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 three open questions) providing a fairly complete picture of the parameterized computational complexity landscape under the two perhaps most natural parameterizations: the distances of the new “similar” cluster graph to (1) the second input graph and to (2) the input cluster graph.

Original languageEnglish
Pages (from-to)1-44
Number of pages44
JournalAlgorithmica
Volume83
Issue number1
DOIs
StatePublished - 1 Jan 2021
Externally publishedYes

Keywords

  • Compromise clustering
  • Correlation clustering
  • Fixed-parameter tractability
  • Goal-oriented clustering
  • Graph-based data clustering
  • Incremental clustering
  • Kernelization
  • Local search
  • Multi-choice knapsack
  • NP-hard problems
  • Parameterized complexity

ASJC Scopus subject areas

  • Computer Science (all)
  • Computer Science Applications
  • Applied Mathematics

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