# Re: Discussion regarding Mr. Diabys algorithm

moustapha.diaby@xxxxxxxxxxxxxxxxxx wrote:
You are simply creating a new, different problem, unless you are able
to infer all the optimal solutions of the "old" problems from those of
the "new" problem.

By the way, I am sorry if I hurt your feelings somewhere. ...Didn't
mean to.

//MD

Dear Prof Diaby,

Yes we are creating a new TSP, where I can mathematically prove the
following 2 points:
1.) The transformed TSP has exactly one optimal tour, even though the
original Generic TSP may have multiple/single optimal tours
2.) The sequence of cities in the optimal tour of the transformed TSP,
is a subset of the sequences of cities of the optimal tours of the
original Generic TSP

Points 1 and 2, correspond to STATEMENT 1 of the original TSP: - "find
the sequence of cities of the optimal tour of the Generic TSP"

In other words, if I give a TSP to Mr. X, and ask Mr. X to produce the
solution to STATEMENT 1, then Mr. X can simply transform the TSP by our
Transformation, and work with the Transformed TSP. The sequence of
cities that Mr. X obtains on the Transformed TSP, will automatically
answer STATEMENT 1 for the original TSP that I gave to Mr. X.

I hope you understood the above paragraph.

We (me & Hofman) will be giving the mathematical proofs for the
above-mentioned points 1 and 2, in our paper. But if you wish me to
prove it right now, I am ready to do it within 3 days. Just let me know
if you want to see the proofs immediately.

By the way, if anyone else in the audience wants to see the proofs now,
then pls let me know....I'll write them in three days time, and post
them in this thread. (But I hope you do not ask me to do that work
right away, cos I am Software Engineer now in a company and we will be
very busy for 1 week, but if you still really want me to show the
proofs urgently, I am ready to do it and show it within 3 days time)

-Deepak

PS: Regarding feelings, come on Prof Diaby, I am surprised to hear you
say that. No, you haven't hurt my feelings anywhere. And I have a high
regard for the originality of your idea of "flows & layers" of your LP
work, which as I said, needs the proof to the "Final Task for Diaby"
that I posted a few posts above.

.

## Relevant Pages

• Re: Discussion regarding Mr. Diabys algorithm
... The sequence of cities in the optimal tour of the transformed TSP, ... then Mr. X can simply transform the TSP by our ...
(comp.theory)
• Re: Discussion regarding Mr. Diabys algorithm
... Dear Mr Hofman, U have given me a very good idea, and I thank you very ... regarding how to TRANSFORM a TSP with many optimal tours, ... The resulting TSP has EXACTLY one optimal tour. ... and addition operation ...
(comp.theory)
• Re: Discussion regarding Mr. Diabys algorithm
... The length of the optimal tour in the Transformed TSP is NOT EQUAL to ... the sequence of cities in the optimal tour of the Transformed TSP ... to chip in here and there with small messages, every now and then, but ...
(comp.theory)
• Re: Discussion about transformation TSP to UniqueTSP
... Radoslaw Hofman wrote: ... We can transform every NP problem to HC ... In mine opinion <= is used to show that we are asking for optimal tour ... somehow it escaped me. ...
(comp.theory)
• Re: Discussion regarding Mr. Diabys algorithm
... Our Transformation uses polynomial space and polynomial time. ... The sequence of cities of the optimal tour of the ... is a subset of the sequences of cities of the optimal ... I agree that the length of the optimal tour of the Transformed TSP ...
(comp.theory)