Fully Dynamic Transitive Closure in Plane Dags with One Source and One Sink
نویسنده
چکیده
We give an algorithm for the Dynamic Transitive 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. We also give a lower bound of Ω(logn/ log logn) on the amortised complexity of the problem in the cell probe model with logarithmic word size.
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