Faster Deterministic Worst-Case Fully Dynamic All-Pairs Shortest Paths via Decremental Hop-Restricted Shortest Paths

Shiri Chechik, Tianyi Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Dynamic all-pairs shortest paths is a well-studied problem in the field of dynamic graph algorithms. More specifically, given a directed weighted graph G = (V, E, ω) on n vertices which undergoes a sequence of vertex or edge updates, the goal is to maintain distances between any pair of vertices in V. In a classical work by [Demetrscu and Italiano, 2004], the authors showed that all-pairs shortest paths can be maintained deterministically in amortized Õ(n2) time1, which is nearly optimal. For worst-case update time guarantees, so far the best randomized algorithm has Õ(n3-1/3) time [Abraham, Chechik, Krinninger, 2017], and the best deterministic algorithm needs Õ(n3-2/7) time [Probst Gutenberg, Wulff-Nilsen, 2020]. We provide a faster deterministic worst-case update time of Õ(n3-20/61) for fully dynamic all-pairs shortest paths. To achieve this improvement, we study a natural variant of this problem where a hop constraint is imposed on shortest paths between vertices; that is, given a parameter h, the h-hop shortest path between any pair of vertices s, t ∈ V is a path from s to t with at most h edges whose total weight is minimized. As a result which might be of independent interest, we give a deterministic algorithm that maintains all-pairs h-hop shortest paths under vertex deletions in total update time Õ(n3h + Kn2h2), where K bounds the total number of vertex deletions.

Original languageEnglish
Title of host publication34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023
PublisherAssociation for Computing Machinery
Pages87-99
Number of pages13
ISBN (Electronic)9781611977554
StatePublished - 2023
Event34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023 - Florence, Italy
Duration: 22 Jan 202325 Jan 2023

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume2023-January

Conference

Conference34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023
Country/TerritoryItaly
CityFlorence
Period22/01/2325/01/23

Funding

FundersFunder number
Horizon 2020 Framework Programme
European Research Council
Horizon 2020803118 UncertainENV

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