Talk:Minimum-cost flow problem

relations

Previously, under Relation to other problems, the reduction to maximum flow said it requires all arcs considered to be of the same cost which is untrue. If all arcs have the same positive costs, the algorithm will try to minimize the number of arcs it takes, which is not necessary for the maximum flow problem. I updated this.PurpleMage (talk) 20:43, 4 December 2010 (UTC)

errors

The current version states that setting all costs to zero recovers the maximum flow problem but this would permit anything as a solution because the function being minimized would always be zero. —Preceding unsigned comment added by 91.125.104.198 (talk) 23:05, 26 March 2011 (UTC)

Not true. Zero is a valid. If the function is always zero, then any flow assignment (that satisfies constraints!) is valid. The problem is that in maximum-flow problem, you find out the maximum flow value. But in the minimum-cost flow problem, you need to specify it first (as 'd'). So I guess it can be used to solve a decisive version of maximum-flow. 2A02:168:F609:0:4F70:D338:7795:DADF (talk) 12:09, 13 September 2019 (UTC)

In the section 'relation to other problems' a lower bound $l$ on the edges is mentioned, which is absent from the definition. I'm in favor of including the lower bound in the definition as well.

vital article -- really?

This article is currently marked as a "vital article" but I find that rather unbelievable. Out of 22K articles in mathematics, it seems like this article would be unlikely to rise above low priority, much less leapfrog into the ranks of "vital article". I notice that there are a low of articles on flow that have been marked as vital -- I suspect that some fan of the topic elevated their status, without thinking about their relative status with respect to other topics in mathematics. 67.198.37.16 (talk) 16:15, 6 June 2021 (UTC)