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Topic: binary search with arbitrary or random split
Replies: 17   Last Post: Jul 27, 2012 6:38 AM

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pamela fluente

Posts: 232
Registered: 1/21/06
Re: binary search with arbitrary or random split
Posted: Jul 27, 2012 6:38 AM
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On Jul 27, 9:50 am, Martin Brown <|||newspam...@nezumi.demon.co.uk>
wrote:


> For the purpose of the analysis we pick a given k and decide how the
> algorithm would behave you can then average over all values of k later.
>
> If you want to force this pathetic approach to have something vaguely
> like probabilistic O(logN) behaviour choose P(k) = 1/k and give or take
> some convergence issues that I can't be bothered to work out it will be.


I said that the random variable is n/k ,

Is that really so hard to understand ? That makes a world of
difference,
in case you have not get it yet.

As to the probability space, i see 2 main approaches

- "conditional" (respect to the data array)
- unconditional

In the first case, you would study the problem considering as random
variable n/k alone
in the second case you would study the problem assuming the array x
also to have some join distribution.

so say

- P ( s | x )
- P ( s , x )

they are both meaningful and interesting.

( Other interesting formalizations, may be considering fuzzy data
instead of crisp, and even probabilistic fuzzy. Clearly one would
introduce membership functions. )






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