6 research outputs found
Path-Contractions, Edge Deletions and Connectivity Preservation
We study several problems related to graph modification problems under
connectivity constraints from the perspective of parameterized complexity: {\sc
(Weighted) Biconnectivity Deletion}, where we are tasked with deleting~
edges while preserving biconnectivity in an undirected graph, {\sc
Vertex-deletion Preserving Strong Connectivity}, where we want to maintain
strong connectivity of a digraph while deleting exactly~ vertices, and {\sc
Path-contraction Preserving Strong Connectivity}, in which the operation of
path contraction on arcs is used instead. The parameterized tractability of
this last problem was posed by Bang-Jensen and Yeo [DAM 2008] as an open
question and we answer it here in the negative: both variants of preserving
strong connectivity are -hard. Preserving biconnectivity, on the
other hand, turns out to be fixed parameter tractable and we provide a
-algorithm that solves {\sc Weighted Biconnectivity
Deletion}. Further, we show that the unweighted case even admits a randomized
polynomial kernel. All our results provide further interesting data points for
the systematic study of connectivity-preservation constraints in the
parameterized setting
On the fixed-parameter tractability of the maximum connectivity improvement problem
In the Maximum Connectivity Improvement (MCI) problem, we are given a
directed graph and an integer and we are asked to find new
edges to be added to in order to maximize the number of connected pairs of
vertices in the resulting graph. The MCI problem has been studied from the
approximation point of view. In this paper, we approach it from the
parameterized complexity perspective in the case of directed acyclic graphs. We
show several hardness and algorithmic results with respect to different natural
parameters. Our main result is that the problem is -hard for parameter
and it is FPT for parameters and , the matching number of
. We further characterize the MCI problem with respect to other
complementary parameters.Comment: 15 pages, 1 figur
A survey of parameterized algorithms and the complexity of edge modification
The survey is a comprehensive overview of the developing area of parameterized algorithms for graph modification problems. It describes state of the art in kernelization, subexponential algorithms, and parameterized complexity of graph modification. The main focus is on edge modification problems, where the task is to change some adjacencies in a graph to satisfy some required properties. To facilitate further research, we list many open problems in the area.publishedVersio
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum