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2. Breaking the Sorting Barrier for Directed Single-Source Shortest Paths

   [Submitted on 23 Apr 2025 (v1), last revised 30 Jul 2025 (this version, v2)] · arXiv.org

   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.