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Fully Dynamic All Pairs All Shortest Paths
[article]
2022
arXiv
pre-print
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We consider the all pairs all shortest paths (APASP) problem, which maintains all of the multiple shortest paths for every vertex pair in a directed graph G=(V,E) with a positive real weight on each edge ...
Our method is a generalization and a variant of the fully dynamic algorithm of Demetrescu and Italiano [DI04] for unique shortest path, and it builds on our recent decremental APASP [NPR14]. ...
McQueeney for working on implementing the FULLY-DYNAMIC algorithm described in this paper. ...
arXiv:1412.3852v4
fatcat:7eget5wtrbeqbmm2yzwf4ckkea
Fully dynamic all-pairs shortest paths with worst-case update-time revisited
2017
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
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We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. ...
Introduction In the all-pairs shortest paths (APSP) problem we are interested in computing the distance matrix of a given graph. ...
Fully dynamic algorithms. The study of fully dynamic APSP algorithms for general directed graphs was initiated by King [Kin99] . ...
doi:10.1137/1.9781611974782.28
dblp:conf/soda/AbrahamCK17
fatcat:4qvphbqv6zfchjpywqht656h6y
Fully-Dynamic All-Pairs Shortest Paths: Improved Worst-Case Time and Space Bounds
[chapter]
2020
Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms
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2020 pre-print arXiv:2001.10801v1 fatcat:t7vbx22zbjea5mxlg6niyzzvumOther Versions
Given a directed weighted graph G=(V,E) undergoing vertex insertions and deletions, the All-Pairs Shortest Paths (APSP) problem asks to maintain a data structure that processes updates efficiently and ...
These are the first exact dynamic algorithms with truly-subcubic update time and space usage. ...
Further, we present the first algorithm for the fully-dynamic All-Pairs Shortest Paths problem (even amortized) in weighted graphs that obtains truly sub-cubic time and space usage at the same time 1 . ...
doi:10.1137/1.9781611975994.156
dblp:conf/soda/GutenbergW20b
fatcat:qugtpkckuva2tilhqcbeluk4xi
Fully dynamic all pairs shortest paths with real edge weights
2006
Journal of computer and system sciences (Print)
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We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights. ...
No previous fully dynamic algorithm was known for this problem. ...
Next, in Section 5 we use this data structure to solve fully dynamic all pairs shortest paths in its generality. ...
doi:10.1016/j.jcss.2005.05.005
fatcat:uf2gpex2hrhcpirotvyypnejbm
Average update times for fully-dynamic all-pairs shortest paths
2011
Discrete Applied Mathematics
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We study the fully-dynamic all pairs shortest path problem for graphs with arbitrary nonnegative edge weights. ...
For a random update we show that the expected time per update is bounded by O(n 4/3+ε ) for all ε > 0. If the graph is outside the critical window, we prove even smaller bounds. ...
In this article, we consider the fully-dynamic all-pairs shortest path problem (APSP) for undirected graphs, which is one of the most fundamental problems in dynamic graph algorithms. ...
doi:10.1016/j.dam.2011.02.007
fatcat:uxqljdpy3fexxokix7pode35rq
Average Update Times for Fully-Dynamic All-Pairs Shortest Paths
[chapter]
2008
Lecture Notes in Computer Science
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We study the fully-dynamic all pairs shortest path problem for graphs with arbitrary non-negative edge weights. ...
For a random update we show that the expected time per update is bounded by O(n 4/3+ε ) for all ε > 0. ...
In this article, we consider the fully-dynamic all-pairs shortest path problem (APSP) for undirected graphs, which is one of the most fundamental problems in dynamic graph algorithms. ...
doi:10.1007/978-3-540-92182-0_61
fatcat:vowyqjlnh5at7mdfdzldqqecw4
Fully Dynamic All-Pairs Shortest Paths: Breaking the O(n) Barrier
2014
International Workshop on Approximation Algorithms for Combinatorial Optimization
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In this paper we break a longstanding barrier in the design of fully dynamic all-pairs approximate distance oracles. ...
A fully dynamic approximate distance oracle is a distance reporting data structure that supports dynamic insert edge and delete edge operations. ...
Our Fully Dynamic All-Pairs Shortest Paths As mentioned earlier, we use the decremental distance oracle Dec from Section 4. ...
doi:10.4230/lipics.approx-random.2014.1
dblp:conf/approx/AbrahamCT14
fatcat:wd6y6tvkxvgylpie4qrdiuxuwi
Fully Dynamic (2 + ε) Approximate All-Pairs Shortest Paths with Fast Query and Close to Linear Update Time
2009
2009 50th Annual IEEE Symposium on Foundations of Computer Science
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However, little progress has been made for fully dynamic approximate algorithms. ...
For any pair x, y ∈ V let π(x, y) be the shortest x − y path, and let d(x, y) be the weight of π(x, y). ...
doi:10.1109/focs.2009.16
dblp:conf/focs/Bernstein09
fatcat:larkpeoodrgghprv7rk6v4o5bm
Fully dynamic all pairs shortest paths with real edge weights
Proceedings 2001 IEEE International Conference on Cluster Computing
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We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights. ...
No previous fully dynamic algorithm was known for this problem. ...
Next, in Section 5 we use this data structure to solve fully dynamic all pairs shortest paths in its generality. ...
doi:10.1109/sfcs.2001.959900
dblp:conf/focs/DemetrescuI01
fatcat:pg2n6btemjgrfgpxbvyzfjeaou
Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs
40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
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This paper presents the first fully dynamic algorithms for maintaining all-pairs shortest paths in digraphs with positive integer weights less than b. ...
For exact shortest paths the amortized update time is O(n 2:5 p b log n). ...
For exact all-pairs shortest paths, the amortized update time is O(n 2:5 p b log n). There are no previously known fully dynamic algorithms for general graphs. ...
doi:10.1109/sffcs.1999.814580
dblp:conf/focs/King99
fatcat:xnyzfujzfrdfbepvmekmprqonm
Triangulations
[chapter]
2013
Discrete Mathematics and Its Applications
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Italiano: Experimental
analysis of dynamic all pairs shortest path algorithms.
ACM Transactions on Algorithms 2 (4): 578-601 (2006). ...
Italiano
A New Approach to Dynamic All Pairs Shortest Paths
Journal of the Association for Computing Machinery
(JACM), 51(6), pp. 968-992, November 2004
Experimental study of dynamic NAPSP algorithms ...
Maintaining shortest paths under deletions in weighted directed graphs. In STOC, 725-734, 2013. ...
doi:10.1201/b16132-52
fatcat:wpkdrbdlubhjrocxna6h34nfyi
Algorithmic Techniques for Maintaining Shortest Routes in Dynamic Networks
2007
Electronical Notes in Theoretical Computer Science
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In this paper, we survey algorithms for shortest paths in dynamic networks. ...
Dynamic Shortest Paths In this section we survey the best known algorithms for fully dynamic shortest paths. We start with a formal definition of the fully dynamic all pairs shortest paths problem. ...
Since by Lemma 2.6 locally historical paths include shortest paths, this yields the fastest known algorithm for fully dynamic all pairs shortest paths. ...
doi:10.1016/j.entcs.2006.11.006
fatcat:ss7kxtmk4fah5a5qmpxieln2be
Fully Dynamic Betweenness Centrality
[chapter]
2015
Lecture Notes in Computer Science
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For graphs with ν * = O(n), our algorithms match the fully dynamic all pairs shortest paths (APSP) bounds of Demetrescu and Italiano [8] and Thorup [28] for unique shortest paths, where ν * = n − 1. ...
We present fully dynamic algorithms for maintaining betweenness centrality (BC) of vertices in a directed graph G = (V, E) with positive edge weights. ...
Both of our BC algorithms are obtained through fully dynamic all pairs all shortest paths. ...
doi:10.1007/978-3-662-48971-0_29
fatcat:yh7hl4aapvgijgcajrvbejnqym
Dynamic shortest paths and transitive closure: Algorithmic techniques and data structures
2006
Journal of Discrete Algorithms
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In particular, we consider two fundamental problems: dynamic transitive closure and dynamic shortest paths. ...
This is an annotated bibliography on fully dynamic algorithms for path problems on general directed graphs. ...
Dynamic shortest paths For dynamic shortest paths, King [27] presented a fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with positive integer weights less than C: ...
doi:10.1016/j.jda.2005.12.003
fatcat:dyr5qbndajfqzlppmiojqhen4e
A new approach to dynamic all pairs shortest paths
2003
Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03
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We study novel combinatorial properties of graphs that allow us to devise a completely new approach to dynamic all pairs shortest paths problems. ...
Our approach yields a fully dynamic algorithm for general directed graphs with non-negative real-valued edge weights that supports any sequence of operations in O(n 2 ) 1 amortized time per update and ...
DYNAMIC ALL PAIRS SHORTEST PATHS In this section we show how to exploit the combinatorial properties of uniform paths presented in Section 2 to design a fully dynamic algorithm for maintaining all pairs ...
doi:10.1145/780542.780567
dblp:conf/stoc/DemetrescuI03
fatcat:wvuqqytvfbg65gwnrbgzzl22b4
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