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This paper presents a randomized algorithm for the problem of single-sourceshortest paths on directed graphs with real (both positive and negative) edgeweights. Given an input graph with $n$ vertices and $m$ edges, the algorithmcompletes in $\tilde{O}(mn^{8/9})$ time with high probability. Forreal-weighted graphs, this result constitutes the first asymptotic improvementover the classic $O(mn)$-time algorithm variously attributed to Shimbel,Bellman, Ford, and Moore.

Single-Source Shortest Paths with Negative Real Weights in $\tilde{O}(mn^{8/9})$ Time