English

Parameterized Dynamic Cluster Editing

Discrete Mathematics 2018-12-12 v2

Abstract

We introduce a dynamic version of the NP-hard graph 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) that represents a solution for the first input graph, can we cost-efficiently transform it into a "similar" cluster graph that is a solution for the 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 three open questions) providing a fairly complete picture of the parameterized computational complexity landscape under the two perhaps most natural parameterizations: the distance of the new "similar" cluster graph to (i) the second input graph and to (ii) the input cluster graph.

Keywords

Cite

@article{arxiv.1810.06625,
  title  = {Parameterized Dynamic Cluster Editing},
  author = {Junjie Luo and Hendrik Molter and André Nichterlein and Rolf Niedermeier},
  journal= {arXiv preprint arXiv:1810.06625},
  year   = {2018}
}
R2 v1 2026-06-23T04:40:34.570Z