DeepAI

A Parameterized View on Multi-Layer Cluster Editing

In classical Cluster Editing we seek to transform a given graph into a disjoint union of cliques, called a cluster graph, using the fewest number of edge modifications (deletions or additions). Motivated by recent applications, we propose and study Cluster Editing in multi-layer graphs. A multi-layer graph consists of a set of simple graphs, called layers, that all have the same vertex set. In Multi-Layer Cluster Editing we aim to transform all layers into cluster graphs that differ only slightly. More specifically, we allow to mark at most d vertices and to transform each layer of the multi-layer graph into a cluster graph with at most k edge modifications per layer such that, if we remove the marked vertices, we obtain the same cluster graph in all layers. Multi-Layer Cluster Editing is NP-hard and we analyze its parameterized complexity. We focus on the natural parameters "max. number d of marked vertices", "max. number k of edge modifications per layer", "number n of vertices", and "number l of layers". We fully explore the parameterized computational complexity landscape for those parameters and their combinations. Our main results are that Multi-Layer Cluster Editing is FPT with respect to the parameter combination (d, k) and that it is para-NP-hard for all smaller or incomparable parameter combinations. Furthermore, we give a polynomial kernel with respect to the parameter combination (d, k, l) and show that for all smaller or incomparable parameter combinations, the problem does not admit a polynomial kernel unless NP is in coNP/poly.

• 26 publications
• 33 publications
• 26 publications
• 15 publications
10/18/2019

Cluster Editing parameterized above the size of a modification-disjoint P_3 packing is para-NP-hard

Given a graph G=(V,E) and an integer k, the Cluster Editing problem asks...
03/07/2023

Cops and Robbers on Multi-Layer Graphs

We generalise the popular cops and robbers game to multi-layer graphs, w...
10/15/2018

Parameterized Dynamic Cluster Editing

We introduce a dynamic version of the NP-hard Cluster Editing problem. T...
02/02/2022

A New Temporal Interpretation of Cluster Editing

The NP-complete graph problem Cluster Editing seeks to transform a stati...
12/06/2021

Modification-Fair Cluster Editing

The classic Cluster Editing problem (also known as Correlation Clusterin...
01/01/2019

On the Parameterized Cluster Editing with Vertex Splitting Problem

In the Cluster Editing problem, a given graph is to be transformed into ...
06/26/2020

On 2-Clubs in Graph-Based Data Clustering: Theory and Algorithm Engineering

Editing a graph into a disjoint union of clusters is a standard optimiza...