Abstract: 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 \(O(m+nlogn)\) time bound of Dijkstra’s algorithm on sparse graphs, showing that Dijkstra’s algorithm is not optimal for SSSP.

Breaking the Sorting Barrier for Directed Single-Source Shortest Paths