A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs

Robert Bredereck, Vincent Froese, Marcel Koseler, Marcelo Garlet Millani, André Nichterlein, Rolf Niedermeier
2018 Algorithmica  
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
more » ... is 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. constructing a specific network topology) or "graph realization" problems. Here, our focus is on inserting arcs into a given digraph in order to fulfill certain vertex degree constraints. These problems are typically NP-hard, so we choose parameterized algorithm design for identifying relevant tractable special cases. The main parameter we work with is the maximum in-or outdegree of the newly constructed digraph. To motivate the problems we deal with, consider the following three application scenarios.
doi:10.1007/s00453-018-0494-6 fatcat:24mcugsrujflblsvg5adonymbq