

Canada’s top science prize goes to Stephen Cook - rpledge
http://www.ottawacitizen.com/news/national/Canada+science+prize+goes+computer+math+whiz+Stephen+Cook/8020598/story.html

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mdxn
There are things mentioned in this article that are completely wrong. There
are also comments here that show a complete misunderstanding of the P vs. NP
question in general, but I won't address these.

The constraint problem here with only pairs of incompatible students is a
instance of 2SAT, which is solvable in quadratic time (i.e. in P; note: the
complexity here is the possible number of pairs, not just students). To make
it reside in NP, it has to be at least 3SAT. Essentially, this is equivalent
to also indicating triples of students that are incompatible (while the pairs
of any of the students in the triple may or may not be compatible). Since the
dean explicitly does not provide this information, we are all good and are in
the position of solving this problem efficiently.

Also, Cook did not invent the P vs. NP problem. He is often credited as the
person who first formalized it and studied it to a sufficient degree. The
first mention of the P vs. NP problem I know of is in a letter from Godel to
Von Neumann (<http://rjlipton.wordpress.com/about/>).

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MichailP
Is example about finding accommodation for 100 from 400 students, given in
article, well formulated? Say dean gives you an empty list, then what is so
difficult in selecting 100 random students?

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jtoohill
It is well-formulated. One could come up with instances of other NP-complete
problems that have trivial solutions, like "What if there are only two cities
and one road between them? Then the Traveling Salesman Problem isn't that
hard!" [1]

If the dean gives you a decently sized list, figuring out such an
accommodation is very difficult (it grows exponentially with the number of
students).

[1] <http://en.wikipedia.org/wiki/Travelling_salesman_problem>

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MichailP
Say he gives you a list of 300 students who can't go together in rooms. You
say, good, I will take the remaining 100 students, and give them rooms. It
even has unique solution :)

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paulgb
Any NP-Complete problem will have cases that are trivial. The complexity of
the problems is how they grow in the worst case.

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rfurmani
Correction: every natural NP-complete problem will have easy cases. You can
construct problems for which there is no easy case, which is a shame since I
thought at one point you could use this trait to seperate P and NP

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paulgb
Interesting. How do you need to define "easy" for this to work? Can you give
an example of a problem without an easy solution? Has this class of problem
been studied?

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TimPC
He's a phenomenal lecturer too, I really enjoyed taking both courses I took
from him. Well deserved award!

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g2e
Can't wait for CSC463 !

