information:classification, linguistic:paraphrasing, stylistic:tone
Connection to successive shortest paths

The Hungarian algorithm can be seen to be equivalent to the successive shortest path algorithm for minimum cost flow, where the reweighting technique from Johnson's algorithm is used to find the shortest paths.The implementation from the previous section is rewritten below in such a way as to emphasize this connection; it can be checked that the potentials h {\displaystyle h} for workers 0 … W − 1 {\displaystyle 0\dots W-1} are equal to the potentials y {\displaystyle y} from the previous solution up to a constant offset. When the graph is sparse (there are only M {\displaystyle M} allowed job, worker pairs), it is possibleto optimize this algorithm to run in O (J M + J 2 log W) {\displaystyle O(JM+J^{2}\log W)} time by using a Fibonacci heap to determine w next {\displaystyle w_{\text{next}}} instead of iterating over all W {\displaystyle W} workers to find the one with minimum distance (alluded to here).