eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-08-23
8:1
8:13
10.4230/LIPIcs.MFCS.2024.8
article
Sublinear Time Shortest Path in Expander Graphs
Alon, Noga
1
https://orcid.org/0000-0003-1332-4883
Grønlund, Allan
2
Jørgensen, Søren Fuglede
2
Larsen, Kasper Green
3
2
https://orcid.org/0000-0001-8841-5929
Princeton University, NJ, USA
Kvantify, Aarhus, Denmark
Aarhus University, Denmark
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol306-mfcs2024/LIPIcs.MFCS.2024.8/LIPIcs.MFCS.2024.8.pdf
Shortest Path
Expanders
Breadth First Search
Graph Algorithms