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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... (Update)
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BibTeX entry: (Update)
@techreport{ eppstein93updating,
author = "David Eppstein",
title = "Updating Widths and Maximum Spanning Trees Using the Rotating Caliper Graph",
number = "ICS-TR-93-18",
pages = "21",
year = "1993",
url = "citeseer.ist.psu.edu/eppstein93updating.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
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: staticto -dynamic transfo.. (context) - Bentley, Saxe - 1980
58 Incremental topological flipping works for regular triangula.. (context) - Edelsbrunner, Shah - 1992
57 Scaling and related techniques for geometry problems (context) - Gabow, Bentley et al. - 1984
47 Voronoi diagrams from convex hulls (context) - Brown - 1979
43 Dynamic trees and dynamic point location - Goodrich, Tamassia - 1991
40 Faster algorithms for some geometric graph problems in highe.. - Callahan, Kosaraju - 1993
35 Dynamic Euclidean minimum spanning trees and extrema of bina.. - Eppstein - 1992
34 Fully dynamic point location in a monotone subdivision (context) - Preparata, Tamassia - 1989
33 an Introduction through Randomized Algorithms (context) - Mulmuley - 1993
[Article contains additional citations not shown here]
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