
Solving the P-NP Puzzler  - peter123
http://www.nytimes.com/2009/10/08/science/Wpolynom.html?_r=1
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donaq
I hate to nitpick, but

 _the computing time required to solve them increases exponentially. In other
words, one more city makes the problem 10 times harder._

That's just sloppy.

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Xichekolas
That was my thought initially too... since the number of solutions of a TSP
with n cities is n! ... which grows much faster than c^n (which they are
implying, with c == 10).

But apparently if you solve the TSP using dynamic programming, you can do it
in c^n time (at least according to the Wikipedia page on Big-O notation... I
haven't researched it much further). This is still solidly NP territory, but
would provide a basis for their claim that one city translates into 10 times
harder.

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pgbovine
cool to see mainstream news coverage of a theoretical CS problem. it'd be even
cooler if they described one compelling concrete example of a specific way
that the world would differ if P=NP, or if P!=NP

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nopassrecover
It's funny because in the average CS degree the P=NP problem isn't even
covered (my sample at least all learned about it online). I don't know if I
know a concrete example of a specific way the world would differ either. Maybe
quicker routing, cancer algorithm solving, simulations, broken encryptions
that kind of stuff?

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donaq
Really? Where did you get your CS degree? I thought complexity theory is an
essential part of any algorithms module, and an algorithms module is in turn
an essential part of any CS degree. I'd hate to have to hire a CS grad who
hasn't taken a class in algorithms.

Are you sure you didn't just not turn up that day? >:)

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nopassrecover
We did comprehensive work on algorithm complexity/data structures etc. But the
NP Complete problem itself was never even touched on beyond a side reference
to the travelling salesman problem at best.

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Dilpil
Does anyone know what the relationship between algebraic geometry and P=NP is?

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amichail
[http://blog.computationalcomplexity.org/2008/04/how-to-
prove...](http://blog.computationalcomplexity.org/2008/04/how-to-prove-np-
different-from-p.html)

