Dear Heiner,
I wonder why the Traveling Salesman Problem is said to be NP-hard
although it can be solved by Linear Programming ?
Wikipedia is not the ultimate authority, but even Wikipedia answers your
question (http://en.wikipedia.org/wiki/P_versus_NP_problem):
Because of these factors, even if a problem is shown to be
NP-complete, and even if P ≠ NP, there may still be effective
approaches to tackling the problem in practice. There are algorithms
for many NP-complete problems, such as the knapsack problem, the
travelling salesman problem and the boolean satisfiability problem,
that can solve to optimality many real-world instances in reasonable
time. The empirical average-case complexity (time vs. problem size)
of such algorithms can be surprisingly low.
2) > I am no scientist,
Are you an engineer? Then, relying on good references and strong
arguments should be a second nature to you as well.
I wish I didn't have to say this (but I feel it is a scientist's duty):
Making revolutionary claims (like you did by writing: "I like to assure
all on this mailing list that P = NP") without a proper proof is not
only counterproductive but downright irresponsible.
Best regards,
Leszek
-------- Original Message --------
Subject: Re: [rrg] p=np !
Date: Wed, 07 Sep 2011 04:47:41 -0400 (EDT)
From: heinerhum...@aol.com
To: leszek.lil...@wmich.edu, rrg@irtf.org
I am no scientist, but may be you are ?:
I wonder why the Traveling Salesman Problem is said to be NP-hard
although it can be solved by Linear Programming ?
I appreciate any clarifying info.
Heiner
-----Ursprüngliche Mitteilung-----
Von: Leszek T. Lilien <leszek.lil...@wmich.edu>
An: rrg <rrg@irtf.org>
Verschickt: Mo, 5 Sept 2011 6:59 pm
Betreff: Re: [rrg] p=np !
Heiner,
Are you a scientist or not?
Your message suggests the latter. (A scientist would vive a proper
reference!)
Leszek
-------- Original Message --------
Subject: Re: [rrg] p=np !
Date: Mon, 05 Sep 2011 16:39:23 -0400 (EDT)
From: heinerhum...@aol.com
To: jinc...@gmail.com
CC: rrg@irtf.org
Sorry, I can't.
It is only myself who thinks to have developed a solution for a np-hard
problem. Precisely for the Steiner Tree problem.
A solution by which any possible lever is applied to improve a current
Steiner Tree until no further lever can quench out any more weight
reduction of the tree at all.
I am not a man the press is interested in. Hence I cannot refer to any
press news.
Heiner
-----Ursprüngliche Mitteilung-----
Von: JinHyeock Choi<jinc...@gmail.com>
An: heinerhummel<heinerhum...@aol.com>
Cc: rrg<rrg@irtf.org>
Verschickt: So, 4 Sept 2011 8:17 pm
Betreff: Re: [rrg] p=np !
I like to assure all on this mailing list that P = NP.
You mean
it has been proved that P = NP?
if so, would you provide a pointer to a relevant article?
That could bring forth a huge impact.
best regards
JinHyeock
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