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.

• ${\displaystyle excess(u)}$. 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

It's not clear from the description of relabel or the generic algorithm that the sink should not be relabeled. Is this somehow implied by the algorithm, or should this simply be a precondition to the relabel operation? — Preceding unsigned comment added by 131.159.46.128 (talk) 18:30, 23 January 2017 (UTC)Reply

The article states:

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

My question: shouldn't it be:

• ${\displaystyle \ \sum _{v}f(u,v)=excess(u)\leq 0}$ for all nodes ${\displaystyle u\neq s}$, 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

The article does not explicitly define active node anywhere. Are active nodes those having excess greater than 0?

Auxier (talk) 21:03, 2 December 2017 (UTC)Reply