Re: Discussion regarding Mr. Diabys algorithm



On Nov 13, 10:51 pm, "deepakc" <deep...@xxxxxxxxxxxxxxxx> wrote:
SUBJECT--------A shocking possibility that everybody is 100% correct,
including Diaby

Dear Everyone,

The whole of yesterday night, I was finding it difficult to sleep,
because I was deeply thinking about all the Google Threads about Diaby
(incl this one).

In this article, I would like to share with you about a strong and
shocking possibility that all 4 people (i.e. David Moews, Yannakakis,
Hofman, and Diaby) are 100% right about their works.

I am sure that the above statement sounds confusing, to all those
reading this. But here is a possible explanation, and I would like
everyone to read this including David Moews, and other mathematical
experts.

Just consider the case....what if Diaby found it difficult to put his
entire idea down into mathematica Equations (refered to as exposition).
What if Diaby found it difficult to express his idea into mathematical
constraint Equations, and therefore was not able to completely define
his assignment polytope in mathematical equations. What if Diaby is
still finding it difficult to express his idea concretely into
mathematics.

In the above case, the following events might have taken place:
- Moews might have performed the polytope permutations on the an
incomplete polytope, which was perhaps not what Diaby intended his
actual Assignment polytope to be.
- Radoslaw might have formulated the 32-node TSP, based on an
incomplete polytope, which was perhaps not Diaby's actual Assignment
polytope
- Yannakakis is no doubt absolutely right regarding his Theorem 1, but
Yannakakis never said that the TSP cannot be solved by an asymmetric LP
formulation, which is what Diaby's actual Assignment Polytope is.....an
Asymmetric Assignment Polytope, but which Diaby has so far been
incapable of a good mathematical exposition.

I must honestly confess that I still haven't fully understood Diaby's
paper. And I get the gut feeling....that we need to listen to Diaby
more carefully. We need to read his paper more carefully, not only the
math part of it, but also try to understand deeper as to what is his
"idea" of "flows and layers", that Diaby is trying to formulate.

For your reference I am pasting some email conversations between me and
Diaby, that took place almost two months ago, before I joined this
particular Google thread. I am certain that after you read these, you
might conclude that Diaby is indeed finding it difficult to find a good
mathematical exposition. The email conversations are attached at the
bottom of this Post.

I would like to conclude by saying that.....Perhaps if we could all be
a little bit more attentive to Diaby, and PERHAPS IF WE COULD HELP
DIABY EXACTLY FORMULATE HIS IDEAS INTO MATH, it might lead the entire
mankind into a "black-hole result".....that P=NP.

For that we need to carefully listen to his idea by talking to him
face-to-face, not by looking at his paper, because he might just be
incapable of good mathematical expression or exposition on paper.

Are you ready for the possibility that P=NP ??? I am !!!

-Deepak


Mr. Chermakani:

I am truly impressed by your efforts to be fair-minded. Bravo!

At the risk of repeating myself both Moews' and Hofman's claims are
quite incorrect. ...And in what I think are obvious ways. But, I have
decided that it may be useful to prepare a somewhat detailed response
to Hofman's claim in particular. I will make it public whenever it
is ready.

For your benefit, here are 2 references that may be helpful:

1. Bazaraa, Jarvis, and Sherali, "Linear Programming and Network
Flows" (Wiley: New York, 1990).

2. Nemhauser and Wolsey, "Integer and Combinatorial Optimization"
(Wiley: New York, 1988).

As I explained to you before, I had to introduce some new notions and
terminologies because the related concepts do not exist in the current
body of knowledge. These are the ones that are discussed in some detail
in the paper. But, if you encounter any terminology (such as
"assignment polytope" for example), that you feel needs defining in
the paper but is not, then, I am pretty sure you will find details on
it in at least one of them...

Also, you may notice that my "exposition" follows the standard in
the Mathematical Programming (more or less), as exemplified by the
general style of these references.

//MD

.

Relevant Pages

  • Re: Discussion regarding Mr. Diabys algorithm
    ... Diaby's Algorithm is as follows. ... He formulates the TSP polytope into Assignment polytope, ... vertexes of the TSP polytope. ... But then Diaby does this.....He relaxes ILP to LP. ...
    (comp.theory)
  • Re: Discussion regarding Mr. Diabys algorithm
    ... He formulates the TSP polytope into Assignment polytope, ... vertexes of the TSP polytope. ... But then Diaby does this.....He relaxes ILP to LP. ... this vertex may not be the CONVEX COMBINATION of vertexes of the TSP ...
    (comp.theory)
  • Re: Discussion regarding Mr. Diabys algorithm
    ... He formulates the TSP polytope into Assignment polytope, ... vertexes of the TSP polytope. ... But then Diaby does this.....He relaxes ILP to LP. ... this vertex may not be the CONVEX COMBINATION of vertexes of the TSP ...
    (comp.theory)