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# Cluster Editing in Multi-Layer and Temporal Graphs

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LIPIcs.ISAAC.2018.24.pdf
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## Cite As

Jiehua Chen, Hendrik Molter, Manuel Sorge, and Ondrej Suchý. Cluster Editing in Multi-Layer and Temporal Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 24:1-24:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ISAAC.2018.24

## Abstract

Motivated by the recent rapid growth of research for algorithms to cluster multi-layer and temporal graphs, we study extensions of the classical Cluster Editing problem. In Multi-Layer Cluster Editing we receive a set of graphs on the same vertex set, called layers and aim to transform all layers into cluster graphs (disjoint unions of cliques) that differ only slightly. More specifically, we want to mark at most d vertices and to transform each layer into a cluster graph using at most k edge additions or deletions per layer so that, if we remove the marked vertices, we obtain the same cluster graph in all layers. In Temporal Cluster Editing we receive a sequence of layers and we want to transform each layer into a cluster graph so that consecutive layers differ only slightly. That is, we want to transform each layer into a cluster graph with at most k edge additions or deletions and to mark a distinct set of d vertices in each layer so that each two consecutive layers are the same after removing the vertices marked in the first of the two layers. We study the combinatorial structure of the two problems via their parameterized complexity with respect to the parameters d and k, among others. Despite the similar definition, the two problems behave quite differently: In particular, Multi-Layer Cluster Editing is fixed-parameter tractable with running time k^{O(k + d)} s^{O(1)} for inputs of size s, whereas Temporal Cluster Editing is W[1]-hard with respect to k even if d = 3.

## Subject Classification

##### ACM Subject Classification
• Theory of computation → Fixed parameter tractability
##### Keywords
• Cluster Editing
• Temporal Graphs
• Multi-Layer Graphs
• Fixed-Parameter Algorithms
• Polynomial Kernels
• Parameterized Complexity

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