A Dual Shortest Path Algorithm
Mokhtar S. Bazaraa, R. W. Langley · SIAM Journal on Applied Mathematics · 1974
We describe a procedure for finding a starting dual feasible solution or terminating by showing that such a solution does not exist, i.e., by detecting a negative cycle. This dual solution can then be used to convert the distance matrix into a nonnegative distance matrix where Dijkstra’s algorithm can be used.