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Dynamic maintenance of planar digraphs, with applications

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Abstract

We show that a planarst-graphG admits two total orders on the setV∪E ∪F, whereV, E, andF are respectively the set of vertices, edges, and faces ofG, with ¦V¦ =n. Assuming thatG is to be dynamically modified by means of insertions of edges and expansions of vertices (and their inverses), we exhibit anO(n)-space dynamic data structure for the maintenance of these orders such that an update can be performed in timeO(logn). The discovered structural properties of planarst-graphs provide a unifying theoretical underpinning for several applications, such as dynamic point location in planar monotone subdivisions, dynamic transitive-closure query in planarst-graphs, and dynamic contact-chain query in convex subdivisions. The presented techniques significantly outperform previously known solutions of the same problems.

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Authors and Affiliations

  1. Department of Computer Science, Brown University, 02912, Providence, RI, USA

    Roberto Tamassia

  2. Coordinated Science Laboratory, University of Illinois, 61801, Urbana, IL, USA

    Franco P. Preparata

Authors
  1. Roberto Tamassia
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  2. Franco P. Preparata
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Additional information

Communicated by C. K. Wong.

This work was carried out at the University of Illinois and was supported in part by National Science Foundation Grant ECS-84-10902 and by the Joint Services Electronics Program under Contract N00014-84-C-0149.

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Tamassia, R., Preparata, F.P. Dynamic maintenance of planar digraphs, with applications. Algorithmica 5, 509–527 (1990). https://doi.org/10.1007/BF01840401

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  • DOI: https://doi.org/10.1007/BF01840401

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