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A linear algorithm for the maximal planar subgraph problem

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Algorithms and Data Structures (WADS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 955))

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Abstract

We construct an optimal linear algorithm for the maximal planar subgraph problem: given a graph G, find a planar subgraph G′ of G such that adding to G′ any edge of G not present in G′ leads to a nonplanar graph. Our solution is based on a dynamic graph search procedure and a fast data structure for on-line planarity testing of triconnected graphs. Our algorithm can be transformed into a new optimal planarity testing algorithm.

This work is partially supported by National Scientific Foundation grant CCR-9409191.

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Authors and Affiliations

  1. Department of Computer Science, Rice University, 77251, Houston, TX, USA

    Hristo N. Djidjev

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  1. Hristo N. Djidjev
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Editor information

Selim G. Akl Frank Dehne Jörg-Rüdiger Sack Nicola Santoro

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© 1995 Springer-Verlag Berlin Heidelberg

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Djidjev, H.N. (1995). A linear algorithm for the maximal planar subgraph problem. In: Akl, S.G., Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1995. Lecture Notes in Computer Science, vol 955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60220-8_77

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  • DOI: https://doi.org/10.1007/3-540-60220-8_77

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60220-0

  • Online ISBN: 978-3-540-44747-4

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