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Average Case Analysis of Dynamic Geometric Optimization (1994)  (Make Corrections)  (11 citations)
David Eppstein
SODA: ACM-SIAM Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms)



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Abstract: We maintain the maximum spanning tree of a planar point set, as points are inserted or deleted, in O(log 3 n) time per update in Mulmuley's expected-case model of dynamic geometric computation. We use as subroutines dynamic algorithms for two other geometric graphs: the farthest neighbor forest and the rotating caliper graph related to an algorithm for static computation of point set widths and diameters. We maintain the former graph in time O(log 2 n) per update and the latter in time O(log n) ... (Update)

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BibTeX entry:   (Update)

D. Eppstein. Average case analysis of dynamic geometric optimization. In Proc. 5th Symp. on Discrete Algorithms, pages 77 -- 86, 1994. http://citeseer.ist.psu.edu/article/eppstein94average.html   More

@inproceedings{ eppstein94average,
    author = "Eppstein",
    title = "Average Case Analysis of Dynamic Geometric Optimization",
    booktitle = "{SODA}: {ACM}-{SIAM} Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms)",
    year = "1994",
    url = "citeseer.ist.psu.edu/article/eppstein94average.html" }
Citations (may not include all citations):
1254   Computational Geometry---An Introduction (context) - Preparata, Shamos - 1985
183   A data structure for dynamic trees (context) - Sleator, Tarjan - 1983
182   Skip lists: a probabilistic alternative to balanced trees - Pugh - 1990
127   Maintenance of configurations in the plane (context) - Overmars, van Leeuwen - 1981
118   Data structures for on-line updating of minimum spanning tre.. (context) - Frederickson - 1985
101   Sparsification -- A technique for speeding up dynamic graph .. (context) - Eppstein, Galil et al. - 1992
94   Closest-point problems (context) - Shamos, Hoey - 1975
74   On constructing minimum spanning trees in k-dimensional spac.. (context) - Yao - 1982
60   Decomposable searching problems I: static-to-dynamic transfo.. (context) - Bentley, Saxe - 1980
58   Incremental topological flipping works for regular triangula.. (context) - Edelsbrunner, Shah - 1992
47   Voronoi diagrams from convex hulls (context) - Brown - 1979
43   Dynamic trees and dynamic point location - Goodrich, Tamassia - 1991
34   Fully dynamic point location in a monotone subdivision (context) - Preparata, Tamassia - 1989
33   an Introduction through Randomized Algorithms (context) - Mulmuley - 1993
26   Dynamic maintenance of geometric structures made easy (context) - Schwarzkopf - 1991

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Documents on the same site (http://www.ics.uci.edu/~eppstein/pubs/geom-all.html):   More
Ununfoldable Polyhedra with Triangular Faces - Bern, Demaine, Eppstein, Kuo.. (1999)   (Correct)
Updating Widths and Maximum Spanning Trees using the Rotating.. - Eppstein (1993)   (Correct)
Average Case Analysis of Dynamic Geometric Optimization - Eppstein (1996)   (Correct)

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