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We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs.
An on-line edge-deletion problem
Shimon Even and Yossi Shiloach · 1981
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A data structure for dynamic trees
Daniel Dominic Sleator and Robert Endre Tarjan · 1983
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Incremental algorithms for minimal length paths
Giorgio Ausiello, Giuseppe F. Italiano, Alberto Marchetti-Spaccamela, and Umberto Nanni · 1990
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High-probability parallel transitive-closure algorithms
Jeffrey D. Ullman and Mihalis Yannakakis · 1991
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Fully dynamic biconnectivity and transitive closure
Monika Rauch Henzinger and Valerie King · 1995
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Randomized dynamic graph algorithms with polylogarithmic time per operation
Monika Rauch Henzinger and Valerie King · 1995
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Dynamic trees as search trees via euler tours, applied to the network simplex algorithm
Robert Endre Tarjan · 1997
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Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs
Valerie King · 1999
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Fully dynamic transitive closure: Breaking through the O ( n 2 ) {O}(n^{2}) barrier
Camil Demetrescu and Giuseppe F. Italiano · 2000
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Near-optimal fully-dynamic graph connectivity
Mikkel Thorup · 2000
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Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity
Jacob Holm, Kristian de Lichtenberg, and Mikkel Thorup · 2001
Cited alongside, same era.
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Uri Zwick · 2002
Cited alongside, same era.
Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths
Surender Baswana, Ramesh Hariharan, and Sandeep Sen · 2004
Cited alongside, same era.
A new approach to dynamic all pairs shortest paths
Camil Demetrescu and Giuseppe F. Italiano · 2004
Cited alongside, same era.
Dynamic transitive closure via dynamic matrix inverse (extended abstract)
Piotr Sankowski · 2004
Cited alongside, same era.
Fully dynamic all pairs shortest paths with real edge weights
Dynamic graph connectivity in polylogarithmic worst case time
Bruce M. Kapron, Valerie King, and Ben Mountjoy · 2013
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Faster deterministic fully-dynamic graph connectivity
Christian Wulff-Nilsen · 2013
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Popular conjectures imply strong lower bounds for dynamic problems
Amir Abboud and Virginia Vassilevska Williams · 2014
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Sublinear-time decremental algorithms for single-source reachability and shortest paths on directed graphs
Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai · 2014
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A subquadratic-time algorithm for decremental single-source shortest paths
Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai · 2014
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Improved algorithms for decremental single-source reachability on directed graphs
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Camil Demetrescu and Giuseppe F. Italiano · 2005
Cited alongside, same era.
Improved dynamic reachability algorithms for directed graphs
Liam Roditty and Uri Zwick · 2008
Cited alongside, same era.
Improved dynamic algorithms for maintaining approximate shortest paths under deletions
Aaron Bernstein and Liam Roditty · 2011
Cited alongside, same era.
On dynamic shortest paths problems
Liam Roditty and Uri Zwick · 2011
Cited alongside, same era.
Dynamic approximate all-pairs shortest paths in undirected graphs
Liam Roditty and Uri Zwick · 2012
Cited alongside, same era.
Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai · 2015
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Maintaining shortest paths under deletions in weighted directed graphs
Aaron Bernstein · 2016
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Dynamic approximate all-pairs shortest paths: Breaking the O ( m n ) {O}(mn) barrier and derandomization
Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai · 2016
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Fully dynamic all-pairs shortest paths with worst-case update-time revisited
Ittai Abraham, Shiri Chechik, and Sebastian Krinninger · 2017
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