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Sublinear Time Shortest Path in Expander Graphs

Authors Noga Alon , Allan Grønlund, Søren Fuglede Jørgensen, Kasper Green Larsen

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Author Details

Noga Alon
  • Princeton University, NJ, USA
Allan Grønlund
  • Kvantify, Aarhus, Denmark
Søren Fuglede Jørgensen
  • Kvantify, Aarhus, Denmark
Kasper Green Larsen
  • Aarhus University, Denmark
  • Kvantify, Aarhus, Denmark

Funding

  • Alon, Noga: Supported by NSF grant DMS-2154082.
  • Larsen, Kasper Green: Supported by a DFF Sapere Aude Research Leader Grant No. 9064-00068B.

Cite AsGet BibTex

Noga Alon, Allan Grønlund, Søren Fuglede Jørgensen, and Kasper Green Larsen. Sublinear Time Shortest Path in Expander Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.MFCS.2024.8

Abstract

Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case. However, several works have shown how to solve this problem in sublinear time in expectation when the input graph is drawn from one of several classes of random graphs. In this work, we extend these results by giving sublinear time shortest path (and short path) algorithms for expander graphs. We thus identify a natural deterministic property of a graph (that is satisfied by typical random regular graphs) which suffices for sublinear time shortest paths. The algorithms are very simple, involving only bidirectional breadth first search and short random walks. We also complement our new algorithms by near-matching lower bounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Shortest paths
Keywords
  • Shortest Path
  • Expanders
  • Breadth First Search
  • Graph Algorithms

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