There is a new sorting algorithm a deterministic O(m log2/3 n)-time algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights in the comparison-addition ...

In such cases, the fastest known shortest-path algorithm doesn’t work. For decades, fast algorithms for finding shortest paths on negative-weight graphs have remained elusive.

The key to their breakthrough is a combination of Dijkstra’s algorithm with another algorithm for the shortest-paths problem called Bellman-Ford, which is much slower but does not produce a ...