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Limits RegistryRan Duan, Jiayi Mao, Xiao Mao, Xinkai Shu and Longhui Yin of Tsinghua University gave an O(m log^(2/3) n) deterministic algorithm for directed single-source shortest paths, the first to beat the O(m + n log n) 'sorting barrier' of Dijkstra's algorithm with Fibonacci heaps on sparse directed graphs. It won the STOC 2025 best paper award.
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Ran Duan, Jiayi Mao, Xiao Mao, Xinkai Shu and Longhui Yin of Tsinghua University gave an O(m log^(2/3) n) deterministic algorithm for directed single-source shortest paths, the first to beat the O(m + n log n) 'sorting barrier' of Dijkstra's algorithm with Fibonacci heaps on sparse directed graphs. It won the STOC 2025 best paper award.
Single-source shortest paths on directed graphs with m edges, n vertices and non-negative real weights can be computed deterministically in O(m log^(2/3) n) time in the comparison-addition model.
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Limits Registry. LR-DIRECTED-SSSP-SORTING-BARRIER. Directed shortest paths faster than Dijkstra's sorting barrier. 2026.