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Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs (1999)  (Make Corrections)  (21 citations)
Valerie King
IEEE Symposium on Foundations of Computer Science



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Abstract: This paper presents the first fully dynamic algorithms for maintaining all-pairs shortest paths in digraphs with positive integer weights less than b. For approximate shortest paths with an error factor of (2 + ffl), for any positive constant ffl, the amortized update time is O(n 2 log 2 n= log log n); for an error factor of (1 + ffl) the amortized update time is O(n 2 log 3 (bn)=ffl 2 ). For exact shortest paths the amortized update time is O(n 2:5 p b log n). Query time for... (Update)

Cited by:   More
Fully Dynamic Transitive Closure: - Breaking Through The   (Correct)
Dynamic Approximate All-Pairs Shortest Paths In Undirected Graphs - Roditty, Zwick   (Correct)
Dynamic Shortest Paths Containers - Wagner, Willhalm, Zaroliagis (2003)   (Correct)

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0.6:   A Fully Dynamic Algorithm for Maintaining the Transitive Closure - King, Sagert (1999)   (Correct)
0.3:   An Experimental Study of Dynamic Algorithms for.. - Frigioni, Miller.. (2000)   (Correct)
0.2:   A Software Library of Dynamic Graph Algorithms - Alberts, Cattaneo (1998)   (Correct)

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0.6:   Improved Algorithms for Maintaining Transitive Closure.. - Baswana, Hariharan, Sen (2001)   (Correct)
0.5:   A New Approach to Dynamic All Pairs Shortest Paths - Demetrescu, Italiano (2002)   (Correct)
0.4:   Randomized Dynamic Graph ALgorithms with Polylogarithmic Time .. - Henzinger, King (1995)   (Correct)

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9:   Fully dynamic transitive closure: Breaking through the O - Demetrescu, Italiano - 2000
9:   Fully Dynamic Biconnectivity and Transitive Closure (context) - Henzinger, King - 1995
9:   Matrix multiplication via arithmetic progressions (context) - Coppersmith, Winograd - 1987

BibTeX entry:   (Update)

V. King. Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In Proc. 40th Annual Symposium on Foundations of Computer Science (FOCS'99), pages 81--89, 1999. http://citeseer.ist.psu.edu/article/king99fully.html   More

@inproceedings{ king99fully,
    author = "Valerie King",
    title = "Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs",
    booktitle = "{IEEE} Symposium on Foundations of Computer Science",
    pages = "81-91",
    year = "1999",
    url = "citeseer.ist.psu.edu/article/king99fully.html" }
Citations (may not include all citations):
308   Matrix multiplication via arithmetic progressions (context) - Coppersmith, Winograd - 1990
50   Incremental algorithm for minimal length paths (context) - Ausiello, Italiano et al. - 1990
49   An incremental algorithm for a generalization of the shortes.. - Ramalingam, Reps - 1996
45   Proximity search in databases - Goldman, Shivakumar et al. - 1998
30   Finding paths and deleting edges in directed acyclic graphs (context) - Italiano - 1988
27   Amortized efficiency of a path retrieval data structure (context) - Italiano - 1986
26   Maintenance of transitive closure and transitive reduction o.. - Poutr, van Leeuwen - 1988
26   Lower bounds for fully dynamic connectivity problems in grap.. - Henzinger, Fredman - 1998
26   the computational complexity of dynamic graph problems - Reps, Ramalingam - 1996
22   All pairs shortest paths in weighted directed graphs--exact .. - Zwick - 1998
15   A data structure for arc insertion and regular path finding (context) - Buchsbaum, Kanellakis et al. - 1991
15   A fully dynamic algorithm for maintaining the transitive clo.. - King, Sagert - 1999
9   Experimental analysis of dynamic algorithms for the singleso.. - Frigioni, Ioffreda et al. - 1998
2   Fully dynamic biconnectivity and transtive closure (context) - Henzinger, King - 1995



The graph only includes citing articles where the year of publication is known.


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Maintaining Minimum Spanning Trees in Dynamic Graphs - Henzinger, King (1997)   (Correct)
On Boolean Decision Trees with Faulty Nodes - Claire Kenyon (1994)   (Correct)
Fully Dynamic 2-Edge Connectivity Algorithm in.. - Henzinger, King (1997)   (Correct)

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