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Abstract: We present algorithms for maintaining the biconnected components of a planar graph undergoing repeated dynamic modifications, such as insertions and deletions of edges and vertices. We show how to test at any time whether two vertices belong to the same biconnected component, and how to insert and delete an edge in O(n 2=3 ) time in the worst case, where n is the number of vertices in the graph. The data structure supports also insertions of new vertices and deletions of disconnected vertices... (Update)
Context of citations to this paper: More
.... algorithms improve previous bounds: for 2 and 3 vertex and 3 edge connectivity, the best previous time bound was O(n 2 3 ) amortized [8, 19, 21], while for 4 edge connectivity nothing better than testing the graph from scratch after each update was known. These bounds apply...
.... much attention has been devoted to the dynamic maintenance of connected components [14, 16, 43] and higher connectivity [8, 10, 18, 19, 20, 21, 32, 35, 53], transitive closure [29, 30, 31, 37, 47, 55] planarity [7, 8, 46] shortest paths [2, 5, 13, 39, 44] and minimum spanning...
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12: Data structures for on-line updating of minimum spanning trees (context) - Frederickson - 1985
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BibTeX entry: (Update)
Z. Galil and G. F. Italiano, "Maintaining biconnected components of dynamic planar graphs," Proc. 18th Int. Colloquium on Automata, Languages, and Programming. (1991), 339--350. http://citeseer.ist.psu.edu/galil91maintaining.html More
@inproceedings{ galil91maintaining,
author = "Z. Galil and G. F. Italiano",
title = "Maintaining biconnected components of dynamic planar graphs",
booktitle = "Proc. 18th Int. Colloquium on Automata, Languages and Programming",
series = "Lecture Notes in Computer Science",
volume = "510",
publisher = "Springer-Verlag, Berlin",
pages = "339--350",
year = "1991",
url = "citeseer.ist.psu.edu/galil91maintaining.html" }
Citations (may not include all citations):1450 The Design and Analysis of Computer Algorithms (context) - Aho, Hopcroft et al. - 1974
474 Graph Theory (context) - Harary - 1969
405 Depth first search and linear graph algorithms (context) - Tarjan - 1972
192 Self-adjusting binary search trees (context) - Sleator, Tarjan - 1985
183 A data structure for dynamic trees (context) - Sleator, Tarjan - 1983
118 Data structures for on-line updating of minimum spanning tre.. (context) - Frederickson - 1985
77 An efficient parallel biconnectivity algorithm (context) - Tarjan, Vishkin - 1985
55 Worst case analysis of set union algorithms (context) - Tarjan, van Leeuwen - 1984
50 Maintenance of a minimum spanning forest in a dynamic planar.. - Eppstein, Italiano et al. - 1990
50 line edge deletion problem (context) - Even, Shiloach et al. - 1981
50 Incremental algorithms for minimal length paths (context) - Ausiello, Italiano et al.
40 Maintaining bridge-connected and biconnected components on-l.. (context) - Westbrook, Tarjan - 1989
33 Updating distances in dynamic graphs (context) - Even, Gazit - 1985
31 On finding and updating spanning trees and shortest paths (context) - Spira, Pan - 1975
30 Finding paths and deleting edges in directed acyclic graphs (context) - Italiano - 1988
30 Incremental planarity testing (context) - Di Battista, Tamassia - 1989
27 line computation of transitive closure for graphs (context) - Ibaraki, Katoh - 1983
27 Amortized efficiency of a path retrieval data structure (context) - Italiano - 1986
26 Maintenance of transitive closure and transitive reduction o.. - Poutr'e, van Leeuwen - 1988
23 line graph algorithms with SPQR-trees (context) - Di Battista, Tamassia - 1990
18 A dynamic data structure for planar graph embedding (context) - Tamassia - 1988
18 A dynamization of the all pairs least cost path problem (context) - Rohnert - 1985
16 Fully dynamic algorithms for edge connectivity problems - Galil, Italiano - 1991
15 A data structure for arc insertion and regular path finding (context) - Buchsbaum, Kanellakis et al. - 1990
14 Algorithms for updating minimum spanning trees (context) - Chin, Houk - 1978
14 A topological approach to dynamic graph connectivity (context) - Reif - 1987
6 Fully dynamic techniques for point location and transitive c.. (context) - Preparata, Tamassia - 1988
6 Algorithms and data structures for dynamic graph problems (context) - Westbrook - 1989
4 line maintenance of the connected components of dynamic grap.. (context) - Harel - 1982
4 A dynamic transitive closure algorithm (context) - Yellin - 1988
2 Dynamic maintenance of paths and path expressions in graphs (context) - Ausiello, Marchetti-Spaccamela et al. - 1989
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