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Parametric and Kinetic Minimum Spanning Trees (1998)  (Make Corrections)  (11 citations)
Pankaj Agarwal, David Eppstein, Leonidas J. Guibas, Monika R. Henzinger
IEEE Symposium on Foundations of Computer Science



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Abstract: We consider the parametric minimum spanning tree problem, in which we are given a graph with edge weights that are linear functions of a parameter # and wish to compute the sequence of minimum spanning trees generated as # varies. We also consider the kinetic minimum spanning tree problem, in which # represents time and the graph is subject in addition to changes such as edge insertions, deletions, and modifications of the weight functions as time progresses. We solve both problems in time O(n ... (Update)

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.... points, like the closest pair, width and diameter, clusters, minimum spanning trees or the constrained Delaunay triangulation [10, 94, 6, 1, 32, 4, 55] (see also the work by Roos [87] on Voronoi diagrams for an approach that is closely related to KDS) Kinetic connectivity...

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BibTeX entry:   (Update)

P. K. Agarwal, D. Eppstein, L. J. Guibas, and M. R. Henzinger. Parametric and kinetic minimum spanning trees. In Proc. 39th IEEE Sympos. Found. Comput. Sci., pages 596-- 605, 1998. http://citeseer.ist.psu.edu/agarwal98parametric.html   More

@inproceedings{ agarwal98parametric,
    author = "Pankaj K. Agarwal and David Eppstein and Leonidas J. Guibas and Monika Rauch Henzinger",
    title = "Parametric and Kinetic Minimum Spanning Trees",
    booktitle = "{IEEE} Symposium on Foundations of Computer Science",
    pages = "596-605",
    year = "1998",
    url = "citeseer.ist.psu.edu/agarwal98parametric.html" }
Citations (may not include all citations):
185   Applying parallel computation algorithms in the design of se.. (context) - Megiddo - 1983
183   A data structure for dynamic trees (context) - Sleator, Tarjan - 1983
121   Data structures for mobile data - Basch, Guibas et al. - 1997
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. - 1997
80   Slowing down sorting networks to obtain faster sorting algor.. (context) - Cole - 1987
61   A separator theorem for graphs with an excluded minor and it.. (context) - Alon, Seymour et al. - 1990
54   Ambivalent data structures for dynamic 2-edge-connectivity a.. - Frederickson - 1997
41   Kinetic data structures --- a state of the art report - Guibas - 1998
37   Polylogarithmic deterministic fully-dynamic algorithms for c.. - Holm, de Lichtenberg et al. - 1998
33   the history of the minimum spanning tree problem (context) - Graham, Hell - 1985
33   Verification and sensitivity analysis of minimum spanning tr.. - Dixon, Rauch et al. - 1992
30   Planar separators and parallel polygon triangulation - Goodrich - 1995
27   A randomized linear-time algorithm for finding minimum spann.. - Karger, Klein et al. - 1995
26   Proximity problems on moving points - Basch, Guibas et al. - 1997
26   A simpler minimum spanning tree verification algorithm - King - 1995
23   Faster parametric shortest path and minimum-balance algorith.. - Young, Tarjan et al. - 1991
15   Geometric lower bounds for parametric matroid optimization - Eppstein
13   Maintaining minimum spanning trees in dynamic graphs - Henzinger, King - 1997
13   A faster deterministic algorithm for minimum spanning trees (context) - Chazelle - 1997
12   Improved bounds on planar k-sets and k-levels - Dey - 1998
4   Parametric problems on graphs of bounded tree-width (context) - andez-Baca, Slutzki - 1994
4   Separator based sparsification I: planarity testing and mini.. (context) - Eppstein, Galil et al. - 1996
3   Algorithmic techniques for geometric optimization - Agarwal, Sharir - 1995
2   Clustering for faster network simplex pivots - Eppstein - 1994
1   Parametric combinatorial optimization problems and applicati.. (context) - Katoh - 1991
1   Bicriteria network optimization problems (context) - Katoh - 1992
1   Using sparsification for parametric minimum spanning tree pr.. (context) - andez-Baca, Slutzki et al. - 1996



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