Talk:Push–relabel maximum flow algorithm

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I believe the third condition defining a preflow should read excess(v) (not u) for all nodes v (not u) — Preceding unsigned comment added by 91.17.171.95 (talk) 23:33, 8 February 2012 (UTC)[reply]

I think "Push" :

height(u) = height(v) + 1. Can only send to lower node.

should be changed to

height(u) > height(v). Can only send to lower node.

because height(s) is set to |V| initially.

$excess(u)$ . Sum of flow to and from u.

Is it really a sum? I would call it a difference between those if that's not my wrong sense of English.

--MBIK (talk) 08:07, 26 July 2009 (UTC)[reply]

For the Push thing, it shouldnt be changed, as you can only push flow to lower node whose height is exactly 1 unit smaller than the node from which the push originates. You cannot push from u to v if height(u)-height(v) > 1 because such edges are not a part of the residual graph due to the height function constraints. The only exception to this is sending flow from source to its neighbors but that is considered a part of the initialization and cannot be reproduced during algorithm work.

As for the other question, it is formally defined as a sum of flow to a node, but your proposition seems good to me as it is generally simpler and more intuitive, especially for wiki purposes.

Nikolicdejan (talk) 10:28, 24 October 2009 (UTC)[reply]

Question...

The article states:

$\ \sum _{v}f(u,v)=excess(u)\geq 0$ for all nodes $u\neq s$ . Only the source may produce flow.

My question: shouldn't it be:

$\ \sum _{v}f(u,v)=excess(u)\leq 0$ for all nodes $u\neq s$ , since "only the source may produce flow" and I assume producing is implied by positive numbers, while leakage along the network (the sink) is implied by the negative ones.

Regards, Kleuske (talk) 14:08, 18 May 2012 (UTC)[reply]

Ah, yes. The source sould have a negative excess. Sorry. Kleuske (talk) 14:31, 18 May 2012 (UTC)[reply]