New Algorithm Breaks Dijkstra's Time Complexity for Directed Shortest Paths
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Summary
The article presents a deterministic algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights, achieving a time complexity of $O(m\log^{2/3}n)$. This breakthrough surpasses the long-standing $O(m+n\log n)$ bound of Dijkstra's algorithm, demonstrating its non-optimality for SSSP on sparse graphs.
Key quotes
· 2 pulledThis is the first result to break the $O(m+n\log n)$ time bound of Dijkstra's algorithm on sparse graphs.
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.
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