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.

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 this note we present some computational evidence to suggest that a version of Bellman's shortest-path algorithm outperforms Treesort-Dijkstra's for a certain class of networks ...