Fully Dynamic Planarity Testing in Planar Embedded Graphs (1993)
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BibTeX
@MISC{Italiano93fullydynamic,
author = {Giuseppe F. Italiano and Johannes A. La Poutré and Monika H. Rauch},
title = {Fully Dynamic Planarity Testing in Planar Embedded Graphs},
year = {1993}
}
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Abstract
We present the first data structure to maintain an embedded planar graph under arbitrary edge insertions, arbitrary edge deletions and queries that test whether the insertion of a new edge would violate the planarity of the embedding. Our data structure supports online updates and queries on an n--vertex embedded planar graph in O(log 2 n) worst--case time, it can be built in O(n) time and requires O(n) space. This work was supported in part by ESPRIT BRA ALCOM II under contract no. 7141 and by the Italian MURST Project "Algoritmi, Modelli di Calcolo e Strutture Informative". A preliminary version of this paper was presented at the 1st European Symposium on Algorithms, Bad Honnef, Bonn, Germany [10]. y Dipartimento di Informatica e Sistemistica, Universit`a di Roma "La Sapienza", Roma, Italy. On leave from IBM T.J. Watson Research Center. z Department of Computer Science, Princeton University, Princeton, NJ 08544, USA. The research of this author was supported by a NATO Scienc...
