Computing maximum upward planar subgraphs of single-source embedded digraphs

We show how to compute a maximum upward planar single-source subgraph of a single-source embedded DAG G φ . We first show that finding a maximum upward planar subgraph of a single-source embedded digraph is NP-complete. We then give a new characterization of upward planar single-source digraphs. We...

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Veröffentlicht in:	Journal of combinatorial optimization 2013-04, Vol.25 (3), p.368-392
Hauptverfasser:	Rextin, Aimal, Healy, Patrick
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Convex and Discrete Geometry Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Theory of Computation
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Zusammenfassung:	We show how to compute a maximum upward planar single-source subgraph of a single-source embedded DAG G φ . We first show that finding a maximum upward planar subgraph of a single-source embedded digraph is NP-complete. We then give a new characterization of upward planar single-source digraphs. We use this characterization to present an algorithm that computes a maximum upward planar single-source subgraph of a single-source embedded DAG. This algorithm takes O ( n 4 ) time in the worst case and O ( n 3 ) time on average.
ISSN:	1382-6905 1573-2886
DOI:	10.1007/s10878-010-9373-z