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Subject: Re: Big-O notation

Author: Dann Corbit

Date: 10:57:57 05/09/01

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On May 09, 2001 at 13:48:00, Ricardo Gibert wrote:

>On May 09, 2001 at 13:26:17, Dann Corbit wrote:
>
>>On May 09, 2001 at 13:08:18, Ricardo Gibert wrote:
>>[snip]
>>>In the traveling salesman problem, f(n) is NP rather than P, since there does
>>>*not* exist a constant c sth f(n) = c*P, since n is unbounded.
>>>
>>>It essential to understand the terms bounded, unbounded and infinity in their
>>>proper context.
>>
>>Since there are a finite number of cities, the travelling salesman problem has
>>SUDDENLY BECOME BOUNDED and you have solved question as to whether a polynomial
>>time solution exists.  In fact, by your definition, you have found a solution
>>which is O(1).
>>
>>I imagine the computer science community will be very happy to hear about this.
>>
>>They don't have a nobel prize for computer science, which is probably just as
>>well.
>
>The traveling salesman problem is more than just a practical problem. It is a
>theoretical problem too with independent interest.

Indeed, but the whole reason we analyze algorithms is to see if we can solve
them.

If I have an algorithm that is O(f(n)), I know what size of a problem I can
attack.  If I use the alternative definition that all implementations are O(1),
then all my analysis is for nothing.

big-O analysis is very much a practical science that deals with problems of
manageable size.  That is the very core nature of its purpose.

If we have inifinite inputs, then nothing is solvable -- (well, maybe O(1))
agreed?




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