Sublinear Time Shortest Path in Expander Graphs

TL;DR

This paper introduces simple sublinear time algorithms for shortest path computation in expander graphs, extending previous results from random graphs to a broader deterministic class with matching lower bounds.

Contribution

It provides the first sublinear time shortest path algorithms for expander graphs based on a natural deterministic property, with simple bidirectional BFS and random walks.

Findings

Sublinear time algorithms for shortest paths in expander graphs.

Matching lower bounds demonstrate near-optimality.

Algorithms are simple and rely on bidirectional BFS and random walks.

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.