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Abstract: We compute the k smallest spanning trees of a point set in the planar Euclidean metric in time O(n log n log k +k min(k,n) 1/2 log(k/n)), and in the rectilinear metrics in time O(n log n + n log log n log k + k min(k,n) 1/2 log(k/n)). In three or four dimensions our time bound is O(n 4/3+# + k min(k,n) 1/2 log(k/n)), and in higher dimensions the bound is O(n 2-2/(#d/2#+1)+# + kn 1/2 log n). 1 Introduction The k smallest spanning tree problem for graphs has been studied... (Update)
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.... k k min(k,n) 1 2 ) and for a point set in higher dimensions the time is O(n 2 2 (#d 2# 1) # kn 1 2 ) 8 Proof: In an earlier work [2] we reduced these geometric problems to the general graph problem in these time bounds. # Feder and Mihail [6] use a random walk technique to...
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BibTeX entry: (Update)
D. Eppstein. Tree-weighted neighbors and geometric k smallest spanning trees. Int. J. Comput. Geom. & Appl. To appear. 10 http://citeseer.ist.psu.edu/eppstein92treeweighted.html More
@article{ eppstein94treeweighted,
author = "David Eppstein",
title = "Tree-weighted neighbors and geometric k smallest spanning trees",
journal = "International Journal of Computational Geometry and Applications",
volume = "4",
number = "2",
pages = "229-238",
year = "1994",
url = "citeseer.ist.psu.edu/eppstein92treeweighted.html" }
Citations (may not include all citations):101 Sparsification ---A technique for speeding up dynamic graph .. (context) - Eppstein, Galil et al. - 1992
81 A linear time algorithm for computing the Voronoi diagram of.. (context) - Aggarwal, Guibas et al. - 1987
54 Ambivalent data structures for dynamic 2-edgeconnectivity an.. - Frederickson - 1991
38 Euclidean minimum spanning trees and bichromatic closest pai.. (context) - Agarwal, Edelsbrunner et al. - 1990
15 Two algorithms for generating weighted spanning trees in ord.. (context) - Gabow - 1977
8 Dynamic algorithms for half-space reporting (context) - Agarwal, Eppstein et al. - 1992
5 the spanning trees of weighted graphs - Mayr, Plaxton - 1990
5 minimum spanning trees (context) - Katoh, Ibaraki et al. - 1981
4 th ACM Symp (context) - Agarwal, Matousek et al. - 1992
2 in graphs. 5th Southeast Conf. Combinatorics, Graph Theory a.. (context) - Burns, Ha et al. - 1974
2 IEEE-LCE Politechnico di Milano (context) - Camerini, Fratta et al. - 1974
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