Parameterized Dynamic Cluster Editing

TL;DR

This paper extends the NP-hard Cluster Editing problem to a dynamic setting where input graphs evolve over time, analyzing the complexity of transforming existing cluster solutions into new ones efficiently.

Contribution

It introduces a dynamic model for Cluster Editing, studies six variants, and provides complexity results including fixed-parameter tractability and hardness proofs.

Findings

Six problem variants analyzed for dynamic cluster editing.

Complexity results include fixed-parameter tractability and hardness.

Provides a comprehensive complexity landscape for the dynamic problem.

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.