Talk:Edmonds-Karp algorithm

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In the article, it is stated that "The distinguishing feature is that the shortest augmenting path is used at each step, which guarantees that the computation will terminate." However, as I understand it, the use of the shortest augmenting path ensure a faster running time than using breadth-running time. The terminiation of the computation is also ensured in the other algorithms based on Ford-Fulkerson, and has as such nothing to do with the breadth-first search. I will try to work on this entry at a later stage.--Kristjan Wager 09:52, 31 May 2005 (UTC)

The article is precisely correct! Please don't change it without discussion. --Zero 13:42, 31 May 2005 (UTC)

According to Cormen et al's Introduction to Algorithms, 2nd edition, the breadth-first search is done to reduce the search time from O(E | f ^* | ) to O(VE²) (see pages 658-663). It has nothing as do with ensuring that the algorithm terminates - this is ensured by the principles of the Ford-Fulkerson method.--Kristjan Wager 14:09, 31 May 2005 (UTC)

No, the O(E | f ^* | ) bound only applies if the capacities are integers. If they are arbitrary real numbers, the Ford-Fulkerson method might fail to terminate and can even converge towards the wrong answer. See Ford-Fulkerson algorithm. --Zero 20:08, 31 May 2005 (UTC)

Ok, thank you for clearifying. While I was aware of the problems with Ford-Fulkerson in regards to real numbers, I was unaware that Edmonds-Karp fixed it. Interesting that Cormen et al didn't mention that aspect. I think I need to read the original article. --Kristjan Wager 07:34, 1 Jun 2005 (UTC)

In the figure: Ek-flow 4.png, there is an arrow upside down, please correct it.

The arrow is drawn correctly. What happens here is that flow is "sent back" from E to D. The flow that was going from D to E is redirected to go to F. Klem fra Nils Grimsmo 15:18, 20 November 2006 (UTC)