The algorithm is identical to the [[Ford-Fulkerson algorithm]], except that the search order when finding the augmenting path is defined. The path found must be the shortest path which has available capacity. This can be found by a [[breadth-first search]], as we let edges have unit length. The running time of <math>O(VVE^2 E)</math> is found by showing that the length of the augmenting path found never decreases, that for every time one of the <math>E</math> edge becomes saturated the augmenting path must be longer than last time it was saturated, that a path is at most <math>V</math> long, and can be found in <math>O(E)</math> time. There is an accessible proof in <ref>{{cite book | author = [[Thomas H. Cormen]], [[Charles E. Leiserson]], [[Ronald L. Rivest]] and [[Clifford Stein]] | title = [[Introduction to Algorithms]] | publisher = MIT Press and McGraw-Hill | year = 2001 | id = ISBN 0-262-53196-8 | edition = second edition | chapter = 26.2 | pages = 660-663 }}</ref>.
