G. D. Battista and R. Tamassia. On-line planarity testing. Technical Report CS-89-31, Department of Computer Science, Brown University, 1989.  Home/Search   Document Not in Database   Summary   Related Articles

....28, 34] Dynamic planar graphs arise in communication networks, graphics, and VLSI design, and they occur in algorithms that build planar subdivisions such as Voronoi diagrams. Algorithms have been proposed for maintaining the embedding of a planar graph [29] and for incremental planarity testing [2, 3]. The dynamic minimum spanning tree problem has been considered by Spira and Pan [28] Chin and Houck [7] Frederickson [10] and Gabow and Stallmann [11] Frederickson gives an algorithm based on topology trees that runs in O( p m) time per operation on general graphs, and O( log n) 2 ) ....

....forest in O(1) time, and to determine the spanning tree containing a given vertex, or find the edge of maximum or minimum weight on the tree path between two vertices, in O(log m) time. The edge ordered tree also finds use in the on line planarity testing algorithm of Di Battista and Tamassia [2, 3]. Thus our data structure is fairly general and powerful. The algorithms can be made to run in worst case time O(log m) with the biased tree implementation of dynamic trees [26] We also argue that in our machine model, any algorithm must spend Omega Gammad 1 n) amortized time per operation; we ....

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G. D. Battista and R. Tamassia. On-line planarity testing. Technical Report CS-89-31, Department of Computer Science, Brown University, 1989.

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