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 -node general networks (in which the distances of arcs can be negative). If no negative loop exists, the algorithm requires <!-- MATH $\frac{1}{2}M\left( {N - 1} \right) \\\left( {N - 2} \right),1 < MN - 1$ --> <img width="309" height="45" align="MIDDLE" border="0" src="images/img2.gif" alt="$ \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 <!-- MATH $\frac{1}{2}N\left( {N - 1} \right)\left( {N - 2} \right)$ --> additions and comparisons.