eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-02-09
10:1
10:14
10.4230/LIPIcs.IPEC.2016.10
article
A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs
Bredereck, Robert
Froese, Vincent
Koseler, Marcel
Millani, Marcelo Garlet
Nichterlein, André
Niedermeier, Rolf
There has been intensive work on the parameterized complexity of the typically NP-hard task to edit undirected graphs into graphs fulfilling certain given vertex degree constraints. In this work, we lift the investigations to the case of directed graphs; herein, we focus on arc insertions. To this end, our general two-stage framework consists of efficiently solving a problem-specific number problem transferring its solution to a solution for the graph problem by applying flow computations. In this way, we obtain fixed-parameter tractability and polynomial kernelizability results, with the central parameter being the maximum vertex in- or outdegree of the output digraph. Although there are certain similarities with the much better studied undirected case, the flow computation used in the directed case seems not to work for the undirected case while f-factor computations as used in the undirected case seem not to work for the directed case.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol063-ipec2016/LIPIcs.IPEC.2016.10/LIPIcs.IPEC.2016.10.pdf
NP-hard graph problem
graph realizability
graph modification
arc insertion
fixed-parameter tractability
kernelization