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For the single-source all-destination version of this problem in directed graphs, the previous best algorithm runs in $O(m+n\\log n)$ ($m=|E|$ and $n=|V|$) time, by Dijkstra search with Fibonacci heap [Fredman and Tarjan 1987]. We improve this time bound to $O(m\\sqrt{\\log n})$, thus it is the first algorithm which breaks the time bound of classic Fibonacci heap when $m=o(n\\sqrt{\\log n})$. 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