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Computing a shortest path between two nodes in an undirected unweighted graphis among the most basic algorithmic tasks. Breadth first search solves thisproblem 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 timein expectation when the input graph is drawn from one of several classes ofrandom graphs. In this work, we extend these results by giving sublinear timeshortest path (and short path) algorithms for expander graphs. We thus identifya natural deterministic property of a graph (that is satisfied by typicalrandom regular graphs) which suffices for sublinear time shortest paths. Thealgorithms are very simple, involving only bidirectional breadth first searchand short random walks. We also complement our new algorithms by near-matchinglower bounds.

Sublinear Time Shortest Path in Expander Graphs