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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 1994: Graph-Theoretic Concepts in Computer Science pp 242–255Cite as

On-line convex planarity testing

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 903))

Abstract

An important class of planar straight-line drawings of graphs are convex drawings, where all faces are drawn as convex polygons. A graph is said to be convex planar if it admits a convex drawing. We consider the problem of testing convex planarity in a dynamic environment, where a graph is subject to on-line insertions of vertices and edges. We present on-line algorithms for convex planarity testing with the following performance, where n denotes the number of vertices of the graph: convex planarity testing and insertion of vertices take worst-case time O(1), insertion of edges takes amortized time O(log n), and the space requirement of the data structure is O(n). Furthermore, we give a new combinatorial characterization of convex planar graphs.

Research supported in part by the National Science Foundation under grant CCR-9007851, by the U.S. Army Research Office under grant DAAL03-91-G-0035 and DAAH04-93-0134, by the Advanced Research Projects Agency under contract N00014-91-J-4052, ARPA order 8225, by the NATO Scientific Affairs Division under collaborative research grant 911016, by the Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo and the grant 94.00023.CT07 of the Italian National Research Council, and by the Esprit II BRA of the European Community (project ALCOM).

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Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Italy

    Giuseppe Di Battista & Luca Vismara

  2. Department of Computer Science, Brown University, Italy

    Roberto Tamassia

Authors
  1. Giuseppe Di Battista
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  2. Roberto Tamassia
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  3. Luca Vismara
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Editor information

Ernst W. Mayr Gunther Schmidt Gottfried Tinhofer

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© 1995 Springer-Verlag Berlin Heidelberg

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Di Battista, G., Tamassia, R., Vismara, L. (1995). On-line convex planarity testing. In: Mayr, E.W., Schmidt, G., Tinhofer, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 1994. Lecture Notes in Computer Science, vol 903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59071-4_52

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  • DOI: https://doi.org/10.1007/3-540-59071-4_52

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59071-2

  • Online ISBN: 978-3-540-49183-5

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