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arXiv · 2504.17033

Breaking the Sorting Barrier for Directed Single-Source Shortest Paths

Ran Duan·Jiayi Mao·Xiao Mao·Xinkai Shu·Longhui Yin
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Abstract

We give a deterministic $O(m\log^{2/3}n)$-time algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights in the comparison-addition model. This is the first result to break the $O(m+n\log n)$ time bound of Dijkstra's algorithm on sparse graphs, showing that Dijkstra's algorithm is not optimal for SSSP.

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Ran Duan, Jiayi Mao, Xiao Mao, Xinkai Shu, Longhui Yin. 2025-04-23. Breaking the Sorting Barrier for Directed Single-Source Shortest Paths. https://arxiv.org/abs/2504.17033

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