Fully Dynamic Shortest Paths in Sparse Digraphs

Adam Karczmarz; Piotr Sankowski

doi:10.4230/LIPICS.ICALP.2023.84

Fully Dynamic Shortest Paths in Sparse Digraphs

Data Structures and Algorithms 2024-08-27 v1

Authors: Adam Karczmarz , Piotr Sankowski

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Abstract

We study the exact fully dynamic shortest paths problem. For real-weighted directed graphs, we show a deterministic fully dynamic data structure with $\tilde{O}(mn^{4/5})$ worst-case update time processing arbitrary $s,t$ -distance queries in $\tilde{O}(n^{4/5})$ time. This constitutes the first non-trivial update/query tradeoff for this problem in the regime of sparse weighted directed graphs.

Keywords

dynamic graph algorithms shortest path problem graph algorithm

Cite

@article{arxiv.2408.14406,
  title  = {Fully Dynamic Shortest Paths in Sparse Digraphs},
  author = {Adam Karczmarz and Piotr Sankowski},
  journal= {arXiv preprint arXiv:2408.14406},
  year   = {2024}
}

Comments

This paper describes the main contribution of our ICALP 2023 paper (see DOI). In addition to the current result, the ICALP 2023 paper also claimed a secondary result on fully dynamic reachability in general sparse digraphs that is flawed. This version retracts that claim and contains a discussion of the error. We thank Jan van den Brand for pointing out this issue

Fully Dynamic Shortest Paths in Sparse Digraphs

Abstract

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