NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs
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- Hartung S., Nichterlein A. (2012) NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs. In: Cooper S.B., Dawar A., Löwe B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg
In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match the given sequence. This realization problem is known to be polynomial-time solvable when the graph is directed or undirected. In contrast, we show NP-completeness for the problem of realizing a given sequence of pairs of positive integers (representing indegrees and outdegrees) with a directed acyclic graph, answering an open question of Berger and Müller-Hannemann [FCT 2011]. Furthermore, we classify the problem as fixed-parameter tractable with respect to the parameter “maximum degree”.
Keywordsgraph realization problems combinatorial algorithms parameterized complexity realizing topological orderings
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