A Refutation of Elmasry's $\tilde{O}(m \sqrt{n})$-Time Algorithm for Single-Source Shortest Paths
Data Structures and Algorithms
2025-08-08 v1
Abstract
In this note we examine the recent 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 , where is the number of vertices and 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 .
Keywords
Cite
@article{arxiv.2508.04872,
title = {A Refutation of Elmasry's $\tilde{O}(m \sqrt{n})$-Time Algorithm for Single-Source Shortest Paths},
author = {Sunny Atalig and Marek Chrobak},
journal= {arXiv preprint arXiv:2508.04872},
year = {2025}
}