Mis tak
es ar
e ok!
--
Regards,
Casey
ie. 30? 50? 100?
--
Regards,
Casey
Do you think you are the only person who's time is valuable?
The series of trivial revisions do not fix, nor really even
address, the error. I've little interest in finding where the
same error appears in reworked versions of the same arguments.
> It is all out there in the current version of the paper for you.
> Unfortunatunately, it is my fault that that version has is over your
> head, at a level beyond your abilities to judge, as you said yourself.
What I was not competent to judge was a specific (alleged) proof
in that version of the paper, which invoked the polytope in an
argument about the constraints forcing a TSP solution.
> Given this, your non-sensical opinions do not really matter,
Ah, but my mathematical argument does.
We are working at different goals: you, to make your proof more
clear; me, to explain why your proof is fundamentally wrong.
Perhaps the most constructive comment I can address to you is
don't borrow against the million.
> and I
> cannot see any in continue these fruitless discussions. Sorry.
Yes, definiely; save your time, and ours.
--
--Bryan
No. Even with the small numbers of cities that have been tried, the
resulting LP's are very large scale. So I believe that going to
problems as large as 30 would require significant developments.
Probably, with a more powerful machine, it may be possible to solve up
to 15-city problems without any further developments.
To be specific, the largest number of cities tried is
8, and the first city is constant, so there are 7!
possible paths. As Moustapha Diaby notes: even with
this small number, the resulting LP is very large.
A critical point, in my opinion -- he does not seem
to agree -- is that at the sizes he has tested, the
number of possible paths does not dominate the number
of constraints in his alleged solution.
The complexity of Diaby's alleged solution is a high-order
polynomial. That's fine, as long as it generally solves
the NP-complete problem, in which the number of possible
solutions is exponential. So far, he has demonstrated no
such result. Diaby's implementation has found solutions,
but in all his cases, his method requires more work than
does (exponential-time) search of the possible paths.
--
--Bryan
No. More importantly than what USENET thinks of them, they have not
been accepted by the theoretical computer science community.
Even more important than any community, is the acceptance for
publication in a professional journal since that must go through a
rigorous review process. There is a P = NP claim that has been
publicized on this usenet that appears to be correct to me. Does anyone
know if that claim been refuted or if it has been accepted in a
journal? And if so (either way), where?
Bob.
In my opinion, acceptance by the theoretical computer science community
as a whole is more important than acceptance for publication in a
professional journal. Roughly speaking, the reason is that the more experts
you have involved, the smaller the chance for imperfections in the process
to cause problems.
The whole business with Hsiang's alleged proof of the Kepler conjecture
should cure anyone of undue respect for peer-reviewed publications.
>There is a P = NP claim that has been
>publicized on this usenet that appears to be correct to me. Does anyone
>know if that claim been refuted or if it has been accepted in a
>journal? And if so (either way), where?
Can you be more specific? There are many claims that fit your vague
description.
> Even more important than any community, is the acceptance for
> publication in a professional journal
That's part of what "the community" means.
> In my opinion, acceptance by the theoretical computer science community
> as a whole is more important than acceptance for publication in a
> professional journal. Roughly speaking, the reason is that the more experts
> you have involved, the smaller the chance for imperfections in the process
> to cause problems.
But how do we judge the acceptance/non-acceptance by the whole TCS
community? Moreover, I am sure that some people would say that there
are experts in computational complexity who are not theoretical
computer scientists.
I think journals are meant to be the objective voices/minds within and
across communities. If a claim cannot find acceptance in any reasonably
well-established journal, then it is more than likely that it is
invalid. So the point of its acceptance by the community is moot. On
the other hand if a claim is accepted in a reasonably well-established
journal, then the burden shifts to those in the community who disagree
with it to show that it is wrong. For that reason I think journal
acceptance is more fundamental.
>
> The whole business with Hsiang's alleged proof of the Kepler conjecture
> should cure anyone of undue respect for peer-reviewed publications.
There is no doubt that there are abherrations. But, I think in general
"Type I errors" are the more common ones compared to the "Type II"
errors like the one you are citing.
> Can you be more specific? There are many claims that fit your vague
> description.
This is the one I am referring to:
http://www.business.uconn.edu/users/mdiaby/tsplp.
Bob.
>>Can you be more specific? There are many claims that fit your vague
>>description.
> This is the one I am referring to:
> http://www.business.uconn.edu/users/mdiaby/tsplp.
We've seen several versions of this paper refuted in this newsgroup.
After each refutation, the author revises the paper. But this cycle
can go on forever. I was impressed by the number of folks here
who were willing to spend time poking holes in the first 3 or 4
revisions.
It definitely hasn't been published in a reputable journal since its
impact would send shockwaves through the theory and math
communities.
If the situation is sufficiently murky that one cannot say for sure that it
has been accepted by the whole community, then I say that means it hasn't
been accepted. These sorts of borderline cases are rare, in any event.
Besides, going for an inferior standard just because it's easier to
adjudicate is obviously a mistake.
>Moreover, I am sure that some people would say that there are experts in
>computational complexity who are not theoretical computer scientists.
A quibble. If you insist on being this pedantic, then simply replace
"theoretical computer scientists" by "complexity theorists" in everything
I said.
>I think journals are meant to be the objective voices/minds within and
>across communities.
Sure. Do they live up to this ideal? Not perfectly. Neither, of course,
does the standard I propose, but because there are more people involved, the
chances of error are smaller.
>If a claim cannot find acceptance in any reasonably
>well-established journal, then it is more than likely that it is
>invalid. So the point of its acceptance by the community is moot. On
>the other hand if a claim is accepted in a reasonably well-established
>journal, then the burden shifts to those in the community who disagree
>with it to show that it is wrong. For that reason I think journal
>acceptance is more fundamental.
Well, then, what do you say about Perelman's work on the Poincare
conjecture? He hasn't bothered submitting it to a journal for publication.
The experts have all examined it in great detail and nobody has found
anything wrong. Does this mean that his work is "more than likely invalid"
because it isn't published?
>http://www.business.uconn.edu/users/mdiaby/tsplp.
This one has not been accepted, and David Moews has clearly and ably
punctured it. Diaby's response to Moews shows that he does not even
understand Moews's refutation.
The claim that my paper contradicts Yannakakis re-surfaces again?!
...Wow! I think it is you and your friend Moews who seem to be somewhat
inept at math programming. It is puzzling to me that people of yours
and Moews supposed calibers would continue to argue, after months of
reflecting on it, that a proof that consists of counting the facets of
a polytope does not need to consider a minimal description of that
polytope! I assure you, that is really preposterous. If you don't
believe me on this, then ask one of old professors at MIT who
specializes in Math Programming.
I stand by everything I have repeatedly stated regarding this claim of
Moews'. The argumentation used by Moews to support the claim is invalid
in trivial ways. Yannakakis' results do not apply to the model in my
paper because the model in my paper is not symmetric and cannot be made
to be in the dimension in which it is fully described, unless it is
"puffed up" nonsensically, a la Moews. And, I am sure I have
pointed out quite a few of these kinds of assaults on fundamentals in
Moews argumentation in previous responses.
As I said before, among other things, if you proceed as Moews does, the
implication is that the TSP cannot be formulated as an LP (any LP),
which is quite different from what Yannakakis claims.
As far as my paper is concerned, true it has not yet been accepted.
But, neither has it been rejected, however. In any case, if for some
reason, there is, eventually, some substantive flaw found in it, I will
bet you anything that it will have nothing to do do with your friend
Moews' preposterous claim of contradiction with Yannakakis' results.
I know a couple of these professors pretty well (though maybe not the
"old" ones), in particular Dimitris Bertsimas, Michel Goemans, and
(less well) John Tsitsiklis. What I will do is to suggest to Dimitris
or Michel that they consider assigning, as extra credit homework in one
of their courses, the task of examining your paper. I can't, of course,
guarantee that they will take my suggestion. But if anything comes of
this, I'll keep comp.theory posted.
If you have a constructive proof that P=NP, why don't you just factor the
RSA challenge numbers? Then people will listen to you. Hell, with a
polynomial-time algorithm for cracking any cipher short of a OTP, the world
is your oyster. You could extort or steal arbitrary sums of money from
practically any individual or organization in the world.
I think that if the proof you released were valid, or even suggested a
possible line of research leading to a valid proof, someone would have had
you assassinated by now.
-- Ben
In fairness to Diaby, a constructive proof that P = NP does not necessarily
mean that the algorithm in question will run quickly in practice.
>I think that if the proof you released were valid, or even suggested a
>possible line of research leading to a valid proof, someone would have had
>you assassinated by now.
Once the proof is publicly released, not much is gained by assassinating
the discoverer, if the discoverer is an independent researcher working
alone.
> We've seen several versions of this paper refuted in this newsgroup.
> After each refutation, the author revises the paper. But this cycle
> can go on forever. I was impressed by the number of folks here
> who were willing to spend time poking holes in the first 3 or 4
> revisions.
To set the record straight: my paper has gone through some revisions
since I first posted it about a year ago. Each revision that was
undertaken in response to a discussion in this newsgroup was undertaken
in reponse to a suggestion that more clarification would be helpful.
The timing of some of these coincided with revisions that were in the
process, in response to inquiries from the Associate Editor handling
the refereeing process of the paper. None of the revisions was the
result of "refutation" by anyone (including people in this newsgroup),
as you can see from the brief summary below:
Context of Revision #1
1. moustapha.di...@business.uconn.edu Feb 15, 4:27 pm
Newsgroups: comp.theory
From: moustapha.di...@business.uconn.edu - Find messages by this author
Date: 15 Feb 2005 12:27:28 -0800
Local: Tues, Feb 15 2005 4:27 pm
Subject: P=NP: Linear Programming Formulation of the TSP
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Dear Fellows of the Community:
Some weeks ago, in the process of extending my LP formulation of the
TSP to other combinatorial problems, I found that the model needed some
additional constraints. I have revised the model and paper accordingly.
I would like to invite you, if I may, to take a look at the revised
model and paper at: http://www.business.uconn.edu/users/mdiaby/TSPLP.
Any comments would be highly appreciated. Regards.//MD.
Context of Revision # 2
Patricia Shanahan wrote:
> Clarifying Proposition 2 would clearly tend to increase the
> number of readers who get past that point in the paper.
I WILL TRY TO FIND ANOTHER WAY TO EXPRESS THE IDEA AND DO A POSTING.
> My particular concern was the mapping from a solution to the
> LP problem to a solution to the original TSP problem. In
> order for the proof to be valid, that mapping must not only
> be proved to exist, but must be proved to be computable in
> polynomial time. I couldn't find where that was proved, but
> it may be obvious given proper understanding of Proposition
> 2 and later points that depend on it.
I THINK THIS WILL FOLLOW ONCE YOU UNDERSTAND PROPOSITION 2, SINCE IT IS
WELL ESTABLISHED THAT LP'S CAN BE SOLVED IN POLYNOMIAL TIME.
Context of Revision #3
> [Bryan Olson wrote:]
> The argument for Proposition 3 cites 2.21, 2.22, 2.28, and 2.29
> as if they held for y' (the final "adjusted y"). The latter two
> are not directly constraints, but are proven assuming other
> constraints on y.
OK, I understand your argument. May (be) I need to be more detailed in
the
proof. I will do so in a (minor) revision that will be posted shortly.
> I know a couple of these professors pretty well (though maybe not the
> "old" ones), in particular Dimitris Bertsimas, Michel Goemans, and
> (less well) John Tsitsiklis.
I meant "old" in the sense of "former."
A friend of mine called to my attention that my first response to Dr.
Chow had a very bad typo in it. Indeed, instead of "ask one of old
professors at MIT..." what I intended to write is "ask one of *your*
old professors at MIT..." in the sense of "ask one of your former
professors..."
To be sure, I hold all my colleagues at MIT in the highest regard. Each
of them that I know of has earned his standing as a pillar of the
profession, and the ones who are senior to me in the profession in
particular, have always been (and continue to be) models for me.
So this is simply the case of a very unfortunate typo.
Well, that's arguable, to say the least. Certainly no one has
refuting it to the point of showing that its conclusion is
false.
The last version to which I responded failed to prove what it
claimed to prove. It relied upon conditions that did not hold.
[...]
>>[Bryan Olson wrote:]
>>The argument for Proposition 3 cites 2.21, 2.22, 2.28, and 2.29
>>as if they held for y' (the final "adjusted y"). The latter two
>>are not directly constraints, but are proven assuming other
>>constraints on y.
>
> OK, I understand your argument. May (be) I need to be more detailed in
> the
> proof. I will do so in a (minor) revision that will be posted shortly.
No minor revision that corrected the error ever appeared. The
version available now makes some claims in the domain of linear
programming that I am not competent to judge. Previous versions
simply claimed a reduction to linear programming, so all that
readers needed to know about linear programming wass that it is
polynomial time. Alas, the reduction was in error.
--
--Bryan
The proof in question was actually correct. But perhaps, it needed to
be more detailed as I stated in my reply to you then. But, it is clear
that you jumped to conclusions by equating my statement "I understand
your argument" with "I agree with your argument." But those are two
different statements.
I had considered the point you made when I was writing the proof in
question, and had decided the level of detail in it had been
sufficient. So, when you made the point, I took that as an indication
that I might have had misjudged the appropriateness of the level of
detail. That is why I responded to you the way I did, in the spirit of
being constructive (instead of argumentative).
> No minor revision that corrected the error ever appeared.
The minor point I was planning to include in the paper is that if you
subtract balance flows from other balanced flows, the resulting flows
must remain balanced. That flows could not become negative as a result
of the procedure I had in the proof because each component that would
have been subtracted as suggested in the proof would have needed to be
appropriately "traced" through the network using the z-variables, as I
had suggested to you in one of our previous communications through this
newsgroup. But, I felt it was pointless to spend time arguing this
online, since I had decided I was going to include more details in the
proof itself.
> version available now makes some claims in the domain of linear
> programming that I am not competent to judge. Previous versions
> simply claimed a reduction to linear programming, so all that
> readers needed to know about linear programming wass that it is
> polynomial time. Alas, the reduction was in error.
In the process of including more details in the proof in question as
discussed above, I decided it would be better altogether, to be as
thorough as possible. So, I took a more direct, "brute-force" route
(so to speak).
There is absolutely no new claim about linear programming in the paper,
since you started posting on it. The essence of paper has remained
exactly the same. The only difference is the level of detail. I am
sorry if you feel that because of this, the work is now beyond your
ability to judge it.
Whether or not you equate the statements, the reliance of the
proof on properties that do not hold for the objects in
question, means that it is incorrect.
> The minor point I was planning to include in the paper is that if you
> subtract balance flows from other balanced flows, the resulting flows
> must remain balanced.
Alas, that doesn't work. "Flows" are not well defined. If we
think of flows simply as paths from source to sink, that's not
strong enough to solve TSP. If we think of flows as also
distinguishing the commodity flowing on the path, then the
constraints are not strong enough to uniquely identify a set of
flows.
> That flows could not become negative as a result
> of the procedure I had in the proof because each component that would
> have been subtracted as suggested in the proof would have needed to be
> appropriately "traced" through the network using the z-variables, as I
> had suggested to you in one of our previous communications through this
> newsgroup.
And I explained why that does not work. The "tracing" is
ambiguous, because more than one set of distinguishable flows on
c.a.s.s. path can satisfy the contraints. I wrote:
There are M! c.a.s.s. paths. Any set of (non-negative) flows
on those paths, such that the total flow is one, forms
exactly one feasible solution. We have M! - 1 degrees of
freedom in creating a legal set of c.a.s.s. path flows. A
feasible solution gives us only polynomial many (order
M**14) equations, so we cannot in general solve for M!
unknowns. There just isn't enough information in a feasible
solution.
The number-of-unknowns argument proves that the recursive
retrieval cannot, in general, reconstruct the set of
c.a.s.s. path flows (even assuming the feasible solution is
a set of c.a.s.s. path flows). Intuitively, where it fails
is that the feasible solution doesn't distinguish each
c.a.s.s. path as its own commodity.
I may have been off on the number of constraints being order
M**14, but many as there are, it's polynomial. There is no way
to distinguish a unique solution for M!-1 unknowns with
polynomially-many linear equations.
--
--Bryan
We are running around in circles, and I definitely don't have the time.
It is all out there in the current version of the paper for you.
Unfortunatunately, it is my fault that that version has is over your
head, at a level beyond your abilities to judge, as you said yourself.
Given this, your non-sensical opinions do not really matter, and I
cannot see any in continue these fruitless discussions. Sorry.
>
> --
> --Bryan
moustap...@business.uconn.edu wrote:
>
> We are running around in circles, and I definitely don't have the time.
> It is all out there in the current version of the paper for you.
> Unfortunately, it is *not* my fault that that version is over your
> head, at a level beyond your abilities to judge, as you say yourself.
> Given this, your non-sensical opinions do not really matter, and I
> cannot see any *benefit* in continuing these fruitless discussions. Sorry.
>