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Abstract: In previous work we introduced sparsification, a technique that transforms fully dynamic algorithms for sparse graphs into ones that work on any graph, with a logarithmic increase in complexity. In this work we describe an improvement on this technique that avoids the logarithmic overhead. Using our improved sparsification technique, we keep track of the following properties: minimum spanning forest, best swap, connectivity, 2-edge-connectivity, and bipartiteness, in time O(n 1/2 ) per ... (Update)
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...case cost of O( # m) per update His data structure permitted connectivity queries to be answered in O(1) time. In 1992, Eppstein et al. [3, 4] improved the update time to O( # n) using the sparsification technique. If only edge insertions are allowed, the Sleator Tarjan dynamic...
...m be the number of edges and n be the number of vertices in the graph. Previous to this work, the best update time was O(min(m 2 3 , n ) [11, 2] with a constant query time. This paper presents an algorithm with O( # m log n) update time and constant query time. Subsequently, the...
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11: Sparsification --- A Technique for Speeding up Dynamic Algorithms (context) - Eppstein, Galil et al. - 1996
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BibTeX entry: (Update)
D. Eppstein, Z. Galil, and G. F. Italiano. Improved sparsification. Technical Report 93-20, Dept. of Inf. and Comp. Sc., Univ. of Calif., Irvine, CA 92717, 1993. http://citeseer.ist.psu.edu/eppstein93improved.html More
@techreport{ eppstein93improved,
author = "David Eppstein and Zvi Galil and Giuseppe F. Italiano",
title = "{Improved sparsification}",
number = "93-20",
year = "1993",
url = "citeseer.ist.psu.edu/eppstein93improved.html" }
Citations (may not include all citations):405 Depth-first search and linear graph algorithms (context) - Tarjan - 1972
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
77 Dividing a graph into triconnected components (context) - Hopcroft, Tarjan - 1973
54 Ambivalent data structures for dynamic 2-edgeconnectivity an.. - Frederickson - 1991
25 Separator based sparsification for dynamic planar graph algo.. (context) - Eppstein, Galil et al. - 1993
20 Fully dynamic biconnectivity in graphs (context) - Rauch - 1992
20 line maintenance of the four-connected components of a graph (context) - Kanevsky, Tamassia et al. - 1991
17 Balanced matroids (context) - Feder, Mihail - 1992
8 Dynamic algorithms for half-space reporting (context) - Agarwal, Eppstein et al. - 1992
7 smallest spanning trees (context) - Eppstein - 1992
4 Algorithms and data structures for an expanded family of mat.. (context) - Frederickson, Srinivas - 1989
1 Tree-weighted neighbors and geometric k smallest spanning tr.. - Eppstein
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