Volume 726 of the series Lecture Notes in Computer Science pp 3748
Optimal upward planarity testing of singlesource digraphs
 Paola BertolazziAffiliated withIASICNR Viale Manzoni
 , Giuseppe Di BattistaAffiliated withDip. di Informatica e Sistemistica, Università di Roma “La Sapienza”
 , Carlo ManninoAffiliated withDip. di Statistica, Università di Roma “La Sapienza”
 , Roberto TamassiaAffiliated withDept. of Computer Science, Brown University
Abstract
A directed graph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in software engineering, project management, and visual languages. In this paper we investigate upward planarity testing of singlesource digraphs: we provide a new combinatorial characterization of upward planarity, and give an optimal algorithm for upward planarity testing. Our algorithm tests whether a singlesource digraph with n vertices is upward planar in O(n) sequential time, and in O(log n) time on a CRCW PRAM with n log log n/log n processors, using O(n) space. The algorithm also constructs an upward planar drawing if the test is successful. The previous best result is an O(n ^{2})time algorithm by Hutton and Lubiw. No efficient parallel algorithms for upward planarity testing were previously known.
 Title
 Optimal upward planarity testing of singlesource digraphs
 Book Title
 Algorithms—ESA '93
 Book Subtitle
 First Annual European Symposium Bad Honnef, Germany September 30–October 2, 1993 Proceedings
 Pages
 pp 3748
 Copyright
 1993
 DOI
 10.1007/3540572732_42
 Print ISBN
 9783540572732
 Online ISBN
 9783540480327
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 726
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Paola Bertolazzi ^{(1)}
 Giuseppe Di Battista ^{(2)}
 Carlo Mannino ^{(3)}
 Roberto Tamassia ^{(4)}
 Author Affiliations

 1. IASICNR Viale Manzoni, 30  00185, Roma, Italy
 2. Dip. di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Salaria, 113  00198, Roma, Italy
 3. Dip. di Statistica, Università di Roma “La Sapienza”, P.le A. Moro, 5  00185, Roma, Italy
 4. Dept. of Computer Science, Brown University, 029121910, Providence, RI
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