An algorithm for finding shortest routes from all source nodes to a given destination in general networks

This paper presents an algorithm for finding all shortest routes from all nodes to a given destination in $N$-node general networks (in which the distances of arcs can be negative). If no negative loop exists, the algorithm requires $\frac{1}{2}M\left( {N - 1} \right) \\ \left( {N - 2} \right),1 < MN - 1$, additions and comparisons. The existence of a negative loop, should one exist, is detected after $\frac{1}{2}N\left( {N - 1} \right)\left( {N - 2} \right)$ additions and comparisons.