<p><a href="http://jeffe.cs.illinois.edu/teaching/algorithms/notes/25-maxflowext.pdf" rel="nofollow noreferrer">http://jeffe.cs.illinois.edu/teaching/algorithms/notes/25-maxflowext.pdf</a></p>

<p>There's a very simple reduction from that problem to the maximum flow problem. This is simply called "maximum flow with edge demands".</p>

CC BY-SA 3.0
2017-03-26T16:29:30.890Z
The link given is for checking if the flow is feasible, i.e. minimum flow.
evil999man
CC BY-SA 4.0
2013-10-19T20:18:36.163Z
2018-11-26T21:25:16.813Z
2018-11-26T21:25:16.813Z
rahulmehta95
<p>The formal prolem is called: "Maximum Flows with Edge Demands" and it's available here: <a href="http://jeffe.cs.illinois.edu/teaching/algorithms/notes/25-maxflowext.pdf" rel="nofollow noreferrer">http://jeffe.cs.illinois.edu/teaching/algorithms/notes/25-maxflowext.pdf</a></p>

CC BY-SA 4.0
2018-11-26T21:24:40.933Z
Welcome to CS.SE!  This duplicates an existing answer.  I'm not sure there is much value in repeating the information already available in an existing answer without adding anything new.  If the purpose was to provide an updated link, a better way to do that is by suggesting an edit (using the 'suggest an edit' link under the answer) to update the link.
D.W.
CC BY-SA 4.0
2018-11-25T22:10:28.410Z
2018-11-25T22:10:28.410Z
Adrian Bona
<p>I have built a max network flow graph that carries certain amount of people from a source to a destination. Now, I'd like to attach a lower bound $l_(e_)$ constraint to each edge $e$. But I don't know what algorithm to use and how to analyze its complexity. Here's the graph:</p>

<p><img src="https://i.sstatic.net/inzm3.png" alt="enter image description here"></p>

<graph-theory><graph-algorithms>
Algorithm for Max Network Flow with lower bounds and its complexity
Jon Adam
# Algorithm for Max Network Flow with lower bounds and its complexity

(Asked by: username_0 on 2013-10-19)

I have built a max network flow graph that carries certain amount of people from a source to a destination. Now, I'd like to attach a lower bound $l\_(e\_)$ constraint to each edge $e$. But I don't know what algorithm to use and how to analyze its complexity. Here's the graph:

![enter image description here](https://i.sstatic.net/inzm3.png)

**Tags:** graph-theory, graph-algorithms

---

## 2 answers

### Answer by username_1 on 2013-10-19. Score: 5

<http://jeffe.cs.illinois.edu/teaching/algorithms/notes/25-maxflowext.pdf>

There's a very simple reduction from that problem to the maximum flow problem. This is simply called "maximum flow with edge demands".

> **Comments:**
> **username_2**: The link given is for checking if the flow is feasible, i.e. minimum flow.  

---

### Answer by username_3 on 2018-11-25. Score: -1

The formal prolem is called: "Maximum Flows with Edge Demands" and it's available here: <http://jeffe.cs.illinois.edu/teaching/algorithms/notes/25-maxflowext.pdf>

> **Comments:**
> **username_4**: Welcome to CS.SE!  This duplicates an existing answer.  I'm not sure there is much value in repeating the information already available in an existing answer without adding anything new.  If the purpose was to provide an updated link, a better way to do that is by suggesting an edit (using the 'suggest an edit' link under the answer) to update the link.  

---

