Fully Dynamic Shortest Paths in Sparse Digraphs
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.14406
- arXiv:
- arXiv:2408.14406
- Bibcode:
- 2024arXiv240814406K
- Keywords:
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- Computer Science - Data Structures and Algorithms
- E-Print:
- 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