Module 5: Networks (problem=cuts)

[jasoN-]

Further never had me thinking too long to solve a problem.
This was swell until I met the problem: Network cuts.

If anyone can explain to me how to draw out all the cuts to a specific network I would appreciate it. (I can calculate capacities of cuts, but not determine the cut itself)

Example:
Consider the network (attached).
Draw up a table listing all the cuts, and the capacity of each cut.

Solution has 6 cuts. If I drew each possible cut I can find around 8.

I really do hate further because of these illogical childsplay-like solutions, which I'm failing to solve.

A cut is defined as a collection of edges that, if removed from the directed graph, produces a zero flow between the start (S) and the terminal (T).

According to this definition, why are my 7th and 8th cut diagrams (2nd .png) not valid in the solution?
According to this definition, why can't we do random squiggly-line cuts everywhere (ie. a cut going up and down, etc)
Someone enlighten me please

[jasoN-]

Bump for desperate need of assistance!

[_avO]

In addition to this guy's question, how do you determine when the cut = 0 as opposed to the preempted number 

[crayolé]

Your 7th is the same as your 1st cut

Your 2nd cut is the same as your 3rd cut

When you draw your cuts through multiple edges you don't have to count every single one of them.

E.g. Say your cut went through 4 edges, however, if only two of those edges(after removing) would result in no flow from the start to finish, then you would only count those two edges in the cut

Your first diagram is cutting SA and SC
Your 7th diagram is also only cutting SA and SC - all the other cuts don't count because you've already restricted the flow from thsoe two cuts alone.

If you need any more help feel free to ask

[plato]

In addition to this guy's question, how do you determine when the cut = 0 as opposed to the preempted number 

Try shading in all the region to the left, or source side, of a cut. This region must include the source of the total flow.
You then ignore any flow that crosses from the unshaded side of the cut to the shaded side of the cut.

[jasoN-]

Ah, thanks crayola for clearing that up , the book doesn't explain the restrictions of cuts.
I'd karma you but you know (looks at post count) :/

[crayolé]

Haha yeah essentials was really ambiguous and crap overall with cuts. I didn't understand it either for agess.

Networks is such a bitch, practice is a must in this module

If you need anything else feel free to ask yeah?

[Gloamglozer]

This module in Essentials is absolute epic fail.  I used Essentials back in year 12 and I just did not understand it.  My advice would be to get your hands on Maths Quest, although I think from memory there were a few mistakes in it?

I found that Maths Quest explained it a little bit better.