A Refutation of Elmasry's $\tilde{O}(m \sqrt{n})$-Time Algorithm for Single-Source Shortest Paths

Abstract: In this note we examine the paper "Breaking the Bellman-Ford Shortest-Path Bound" by Amr Elmasry, where he presents an algorithm for the single-source shortest path problem and claims that its running time complexity is $\tilde{O}(m\sqrt{n})$, where $n$ is the number of vertices and $m$ is the number of edges. We show that his analysis is incorrect, by providing an example of a weighted graph on which the running time of his algorithm is $\Omega(mn)$.