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Abstract: . We give an algorithm for the DynamicTransitive Closure Problem for planar directed acyclic graphs with one source and one sink. The graph can be updated in logarithmic time under arbitrary edge insertions and deletions that preserve the embedding. Queries of the form `is there a directed path from u to v?' for arbitrary vertices u and v can be answered in logarithmic time. The size of the data structure and the initialisation time are linear in the number of edges. The result enlarges ... (Update)
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...of balanced parentheses [9] We show that all these problems require time Omega Gammame n= log log n) per operation. It is known [8, 12, 15, 20] that this is also a lower bound for reachability in grid graphs. However, grid graphs of constant width allow a reachability...
...Graphs are the object of study in Chap. 4. It includes an efficient dynamic reachability algorithm for a small class of digraphs from [34] and a couple of lower bounds for graph problem that stem from [36] Our third case study is strings, namely strings of properly balanced...
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BibTeX entry: (Update)
RS-94-30 Thore Husfeldt. Fully Dynamic Transitive Closure in Plane Dags with one Source and one Sink. September 1994. 26 pp. http://citeseer.ist.psu.edu/husfeldt94fully.html More
@inproceedings{ husfeldt95fully,
author = "Thore Husfeldt",
title = "Fully Dynamic Transitive Closure in Plane Dags with One Source and One Sink",
booktitle = "European Symposium on Algorithms",
pages = "199-212",
year = "1995",
url = "citeseer.ist.psu.edu/husfeldt94fully.html" }
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