A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs
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.
NP-hard graph problem
graph realizability
graph modification
arc insertion
fixed-parameter tractability
kernelization
10:1-10:14
Regular Paper
Robert
Bredereck
Robert Bredereck
Vincent
Froese
Vincent Froese
Marcel
Koseler
Marcel Koseler
Marcelo Garlet
Millani
Marcelo Garlet Millani
André
Nichterlein
André Nichterlein
Rolf
Niedermeier
Rolf Niedermeier
10.4230/LIPIcs.IPEC.2016.10
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