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Fully Dynamic Shortest Paths and Reachability in Sparse Digraphs

Authors Adam Karczmarz , Piotr Sankowski

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Author Details

Adam Karczmarz
  • University of Warsaw, Poland
  • IDEAS NCBR, Warsaw, Poland
Piotr Sankowski
  • University of Warsaw, Poland
  • IDEAS NCBR, Warsaw, Poland

Funding

  • Karczmarz, Adam: Partially supported by the ERC CoG grant TUgbOAT no 772346.
  • Sankowski, Piotr: Partially supported by the ERC CoG grant TUgbOAT no 772346 and National Science Center (NCN) grant no. 2020/37/B/ST6/04179.

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Adam Karczmarz and Piotr Sankowski. Fully Dynamic Shortest Paths and Reachability in Sparse Digraphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 84:1-84:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICALP.2023.84

Abstract

We study the exact fully dynamic shortest paths problem. For real-weighted directed graphs, we show a deterministic fully dynamic data structure with Õ(mn^{4/5}) worst-case update time processing arbitrary s,t-distance queries in Õ(n^{4/5}) time. This constitutes the first non-trivial update/query tradeoff for this problem in the regime of sparse weighted directed graphs. Moreover, we give a Monte Carlo randomized fully dynamic reachability data structure processing single-edge updates in Õ(n√m) worst-case time and queries in O(√m) time. For sparse digraphs, such a tradeoff has only been previously described with amortized update time [Roditty and Zwick, SIAM J. Comp. 2008].

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
  • Theory of computation → Shortest paths
Keywords
  • dynamic shortest paths
  • dynamic reachability
  • dynamic transitive closure

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