Re: Discussion regarding Mr. Diabys algorithm



To show you a bit of this in different way:

Let us assume that there are flows:

5_5_6->6_6_7->7_7_8->8_8_7

6_5_7....

7_5_8....

....

If you will build every combination of legal flows (no backflow to first arc
in row - as in first and second) and sum them then you will see that on
"upper level" everything is ok. You may see that each row is equivalent to
some y starting with first letters. There is then no illegal y and after
joining them you obtain model.

I don't understand this statement. Can ytou give details?


Same with z but you must build flows omitting first two arcs.

Now if you get enough of such "flows" you may meet all equations.




Think (a little) in such way:

- I assume that you agree that x_isj is not enough

- if you pick one arc then you have n^3 of this insufficient models... when
you add them then you will meet all restrictions for y's

- if you pick 2 arcs then it is n^6 of this insufficient models...

What makes you think that this time it will be different and only correct
TSP solutions will be feasible? For 2 arcs chosen it is still nothing more
then x_isj model... It is enough to prepare large enough instance to show
it.


No, the error you are making here is you are assuming constraints work
in isolation. I am not "thinking" anything. I am relying on the
mathematics in the paper, particularly, Proposition 2.


So please don't write "impossible" - rather show which constraint is
violated in counter example (and I assure you that you cannot show it
because everything is compliant with your model) and prove in formal way
that it cannot exist.

The "formal proof" is Proposition 2. The proof of that proposition is
very detailed in my paper. Can you point out the flaw in it?


When "playing" with sums (and your model summarizes flows) it is difficult
to trace what was taken to sum.

I perfectly agree with this. That is why we must rely on mathematics
instead of computer codes and untested, ad-hoc procedures as you do.
So, it may be more fruitful if you could point out the error(s) in the
theoretical developments in the paper, especially Propositions 2 and 3
that your construct contradicts directly.

.