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Topic: binary search with arbitrary or random split
Replies: 2   Last Post: Jul 25, 2012 7:25 PM

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Ben Bacarisse

Posts: 1,566
Registered: 7/4/07
Re: binary search with arbitrary or random split
Posted: Jul 25, 2012 7:06 PM
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Patricia Shanahan <pats@acm.org> writes:

> On 7/25/2012 9:25 AM, pam wrote:
> ...

>> Should one singularity which causes the least upper bound to raise
>> from O(logn)
>> to "no better than O(n)" be considered in the computational complexity
>> assessment,
>> considered that its probability tends to 0 ?
>>
>> Patricia was saying yes.
>>
>> You were saying, at one point, that stuff with probability 0 should
>> not be considered in the asymptotic analysis.

> ...
>
> Ben, do you agree with the following?
>
> A case can be ignored for calculating worst case complexity if, and only
> if, there exists a natural number N such that the probability of that
> case is zero if the input size is greater than N.
>
> Not tending to zero, not approximately zero, not zero for some large
> inputs, but zero for *all* inputs larger than some finite size.


Is sounds right but you seem to be using "case" in an a way that does
not match my usage. A "case", for me, is one execution of the
algorithm, and the cost for some size is just the maximum cost of all
the possible executions with that input size.

You seem to use "case" to means a particular class of executions (maybe
characterised by some behaviour of the algorithm or some property of the
inputs) rather than single executions. With that meaning, yes, I agree.

--
Ben.



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