Article

Worst-case update times for fully-dynamic all-pairs shortest paths

Author:

Mikkel ThorupAuthors Info & Claims

STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing

Pages 112 - 119

https://doi.org/10.1145/1060590.1060607

Published: 22 May 2005 Publication History

Abstract

We present here the first solution to the fully-dynamic all pairs shortest path problem where every update is faster than a recomputation from scratch in Ω(n³log ⁄n) time. This is for a directed graph with arbitrary non-negative edge weights. An update inserts or deletes a vertex with all incident edges. After each such vertex update, we update a complete distance matrix in Õ(n^2.75) time.

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Cited By

Mao XMohar BShinkar IO'Donnell R(2024)Fully Dynamic All-Pairs Shortest Paths: Likely Optimal Worst-Case Update TimeProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649695(1141-1152)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649695
Haeupler BLong YSaranurak T(2024)Dynamic Deterministic Constant-Approximate Distance Oracles with $n^{\epsilon}$ Worst-Case Update Time2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00121(2033-2044)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00121
Forster SNazari YProbst Gutenberg MSaha BServedio R(2023)Deterministic Incremental APSP with Polylogarithmic Update Time and StretchProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585213(1173-1186)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585213
Show More Cited By

Index Terms

Worst-case update times for fully-dynamic all-pairs shortest paths
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Conferences

STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing

May 2005

778 pages

ISBN:1581139608

DOI:10.1145/1060590

General Chair:
Hal Gabow
University of Colorado
,
Program Chair:
Ronald Fagin
IBM Almaden Research Center

Copyright © 2005 ACM.

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Published: 22 May 2005

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May 22 - 24, 2005

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Mao XMohar BShinkar IO'Donnell R(2024)Fully Dynamic All-Pairs Shortest Paths: Likely Optimal Worst-Case Update TimeProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649695(1141-1152)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649695
Haeupler BLong YSaranurak T(2024)Dynamic Deterministic Constant-Approximate Distance Oracles with $n^{\epsilon}$ Worst-Case Update Time2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00121(2033-2044)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00121
Forster SNazari YProbst Gutenberg MSaha BServedio R(2023)Deterministic Incremental APSP with Polylogarithmic Update Time and StretchProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585213(1173-1186)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585213
Van Den Brand JKarczmarz A(2023)Deterministic Fully Dynamic SSSP and More2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00142(2312-2321)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00142
Karczmarz ASankowski P(2023)Sensitivity and Dynamic Distance Oracles via Generic Matrices and Frobenius Form2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00106(1745-1756)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00106
Hanauer KHenzinger MSchulz C(2022)Recent Advances in Fully Dynamic Graph Algorithms – A Quick Reference GuideACM Journal of Experimental Algorithmics10.1145/355580627(1-45)Online publication date: 13-Dec-2022
https://dl.acm.org/doi/10.1145/3555806
Bernstein AGutenberg MSaranurak T(2022)Deterministic Decremental SSSP and Approximate Min-Cost Flow in Almost-Linear Time2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00100(1000-1008)Online publication date: Mar-2022
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Jin WSun X(2022)Fully Dynamic s-t Edge Connectivity in Subpolynomial Time (Extended Abstract)2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00088(861-872)Online publication date: Mar-2022
https://doi.org/10.1109/FOCS52979.2021.00088
Duan RGu YRen HMarx D(2021)Approximate distance oracles subject to multiple vertex failuresProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458212(2497-2516)Online publication date: 10-Jan-2021
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Bergamaschi THenzinger MGutenberg MWilliams VWein NMarx D(2021)New techniques and fine-grained hardness for dynamic near-additive spannersProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458174(1836-1855)Online publication date: 10-Jan-2021
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