Breaking the Sorting Barrier for Directed Single-Source Shortest Paths

We give a deterministic $O(m{\log }^{2\mathrm{/}3}n)$-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.