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On the Hardness of Finding Temporally Connected Subgraphs of Any Size
Arnaud Casteigts, Christian Komusiewicz, Nils Morawietz
Temporal graphs are graphs whose edges are present only at certain points in time. Reachability in these graphs is defined via temporal paths, in which edges are traversed in incre…
A Parameterized-Complexity Framework for Finding Local Optima
Robert Ganian, Hung P. Hoang, Christian Komusiewicz +1
Local search is a fundamental optimization technique that is both widely used in practice and deeply studied in theory, yet its computational complexity remains poorly understood.…
The Parameter Report: An Orientation Guide for Data-Driven Parameterization
Christian Komusiewicz, Nils Morawietz, Frank Sommer +1
A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered paramete…
Parameterized Local Search for Max -Cut
Jaroslav Garvardt, Niels Grüttemeier, Christian Komusiewicz +1
In the NP-hard Max -Cut problem, one is given an undirected edge-weighted graph and aims to color the vertices of with colors such that the total weight of edges wit…
Complexity of Local Search for Euclidean Clustering Problems
Bodo Manthey, Nils Morawietz, Jesse van Rhijn +1
We show that the simplest local search heuristics for two natural Euclidean clustering problems are PLS-complete. First, we show that the Hartigan--Wong method for -Means cluste…
Multi-Parameter Analysis of Finding Minors and Subgraphs in Edge Periodic Temporal Graphs
Emmanuel Arrighi, Niels Grüttemeier, Nils Morawietz +2
We study the computational complexity of determining structural properties of edge periodic temporal graphs (EPGs). EPGs are time-varying graphs that compactly represent periodic b…