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Maintenance of a Minimum Spanning Forest in a Dynamic Plane Graph
, 1992
"... We give an efficient algorithm for maintaining a minimum spanning forest of a plane graph subject to online modifications. The modifications supported include changes in the edge weights, and insertion and deletion of edges and vertices which are consistent with the given embedding. Our algorithm r ..."
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Cited by 68 (26 self)
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We give an efficient algorithm for maintaining a minimum spanning forest of a plane graph subject to online modifications. The modifications supported include changes in the edge weights, and insertion and deletion of edges and vertices which are consistent with the given embedding. Our algorithm runs in O(log n) time per operation and O(n) space.
Fully Dynamic Transitive Closure in Plane Dags with One Source and One Sink
, 1994
"... 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 ..."
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Cited by 2 (2 self)
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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###26 n/ log log n) on the amortised complexity of the problem in the cell probe model with logarithmic word size.
Computational Complexity of Dynamic Problems
"... . This progress report surveys some of my scientific work on part A of the Ph.D.programme at the Computer Science Department of the University of Aarhus. I give a surveylike introduction to the field of Complexity Theory to which my results bear relevance. I give a general account of my contri ..."
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. This progress report surveys some of my scientific work on part A of the Ph.D.programme at the Computer Science Department of the University of Aarhus. I give a surveylike introduction to the field of Complexity Theory to which my results bear relevance. I give a general account of my contributions to the field, including the the Dynamic Transitive Closure Problem for spherical stgraphs, the Dynamic Circuit Value Problem, and some dynamic membership problems for formal languages. Contents I. Introduction 3 1. Dynamic Algorithms 2. Overview II. Reachability 6 1. The parallel world 2. Dynamic algorithms for Reachability 3. Planar dags with one source and one sink 4. The result: a detailed account III. Formal Languages 14 1. Other realms 2. Regular Languages 3. Dyck Languages 4. Deterministic contextfree languages 5. Conclusion and open problems IV. Finite Index Properties on Graphs of Bounded Treewidth 21 1. Introduction 2. Preliminaries 3. Dynamic Algorithms...