An alternative to the Master Theorem?

Question

I've been reading up on the Master Theorem (used for identifying the worst case run times of a certain class of recursive functions [ the divide and conquer type] ).

I looked at the Wikipedia entry and in the Inadmissible section (functions for which the Master Theorem is not applicable), this function was present:

$ T(n) = 2 T (\frac{n}{2}) + \frac{n}{logn} $

I get how it's inadmissible because the value of $ k $ is less than $ 0 $. What I don't get is the justification for this. Why would you have to get the difference between $ f(n) $ and $ n^{log_bn} $? What does this tell you?

Also, is there a way sans master theorem in which I can easily size up a reasonable upper bound for a function like this?

Thanks a bunch!

score 2 · Accepted Answer · answered Oct 17 '13 at 23:53

2

You are right that this cannot be solved using the Master Theorem. I actually had a very similar assignment question when I took an algorithm's course a few terms back, and the way I solved it was using the "Guess & Check" method, in which you expand terms until you notice a pattern, then prove the result by induction. You might also be able to use this: http://en.wikipedia.org/wiki/Akra%E2%80%93Bazzi_method - a generalized version of the Master Theorem.

answered Oct 17 '13 at 23:53

Nizbel99

907

Thanks for the reply Nizbel99. Doing a guess and check was in fact what I was trying to avoid here, but I guess I'm going to have to bite the bullet. ha – tuba09 Oct 18 '13 at 00:25
There is an exact solution to this recurrence at this Math.SE link. – Marko Riedel Oct 19 '13 at 00:46

An alternative to the Master Theorem?

1 Answers1