Breaking the Sorting Barrier for Directed Single-Source Shortest Paths

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 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.