Parameterized Dynamic Cluster Editing

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-ef...

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Bibliographic Details
Published in:Algorithmica Vol. 83; no. 1; pp. 1 - 44
Main Authors: Luo, Junjie, Molter, Hendrik, Nichterlein, André, Niedermeier, Rolf
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2021
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Clustering
Computer Science
Computer Systems Organization and Communication Networks
Data search
Data Structures and Information Theory
Distance measurement
Editing
Graphs
Mathematics of Computing
Parameterization
Theory of Computation
Local search
Goal-oriented clustering
NP-hard problems
Correlation clustering
Incremental clustering
Graph-based data clustering
Compromise clustering
Multi-choice knapsack
Fixed-parameter tractability
Parameterized complexity
Kernelization
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary: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.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-020-00746-y