Computing maximum upward planar subgraphs of single-source embedded digraphs

Aimal Rextin; Patrick Healy

doi:10.1007/s10878-010-9373-z

Computing maximum upward planar subgraphs of single-source embedded digraphs

Aimal Rextin, Patrick Healy

Department of Computer Science & Information Systems

National University of Sciences and Technology Pakistan

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	368-392
Number of pages	25
Journal	Journal of Combinatorial Optimization
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s10878-010-9373-z
Publication status	Published - Apr 2013

Keywords

Graph drawing
Single-source digraphs
Upward planarity

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abstract = "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.",

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AB - 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.

KW - Graph drawing

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Computing maximum upward planar subgraphs of single-source embedded digraphs

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Keywords

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