Graphs Shortcuts: New Bounds and Algorithms (Invited Talk)

Author Merav Parter



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Author Details

Merav Parter
  • Weizmann Institute of Science, Rehovot, Israel

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Merav Parter. Graphs Shortcuts: New Bounds and Algorithms (Invited Talk). In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.4

Abstract

For an n-vertex digraph G = (V,E), a shortcut set is a (small) subset of edges H taken from the transitive closure of G that, when added to G guarantees that the diameter of G ∪ H is small. Shortcut sets, introduced by Thorup in 1993, have a wide range of applications in algorithm design, especially in the context of parallel, distributed and dynamic computation on directed graphs. A folklore result in this context shows that every n-vertex digraph admits a shortcut set of linear size (i.e., of O(n) edges) that reduces the diameter to Õ(√n). Despite extensive research over the years, the question of whether one can reduce the diameter to o(√n) with Õ(n) shortcut edges has been left open. In this talk, I will present the first improved diameter-sparsity tradeoff for this problem, breaking the √n diameter barrier. Specifically, we show an O(n^ω)-time randomized algorithm for computing a linear shortcut set that reduces the diameter of the digraph to Õ(n^{1/3}). I also present time efficient algorithms for computing these shortcuts and explain the limitations of the current approaches. Finally, I will draw some connections between shortcuts and several forms of graph sparsification (e.g., reachability preservers, spanners). Based on a joint work with Shimon Kogan (SODA 2022, ICALP 2022, FOCS 2022, SODA 2023).

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • Shortcuts
  • Spanners
  • Distance Preservers

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