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I'm facing a question with comparison networks. Find second and third min.

Posted on 2014-03-23
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Last Modified: 2014-03-24
I'm asked to
a. prove that depth of a comparison network that will find values of seond and third minimum is Omega(lg n).  
b. build such a network.

I need a hand here.

http://en.wikipedia.org/wiki/File:Six-wire-bubble-sorting-network.svg
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Question by:aboo_s
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Accepted Solution

by:
TommySzalapski earned 300 total points
ID: 39949332
Could you do it for the first minimum?
Do that and then remember that Omega(3 lg n) = Omega(lg n)
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Author Comment

by:aboo_s
ID: 39949460
And why is finding the first minimum is Omega(n) in network depth?
You need only n/2 comparators for that.
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LVL 84

Assisted Solution

by:ozo
ozo earned 200 total points
ID: 39949464
Omega(n) = Omega(n/2) but the depth of a comparison network for the first minimum is Omega(lg n)
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LVL 10

Author Comment

by:aboo_s
ID: 39949613
ozo:
I know that the depth is Omega(lg n), I'm asked to prove that. And build such a network.
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Author Comment

by:aboo_s
ID: 39949616
I have got the answer.
If anybody likes to hear it, I'll be more than happy.
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LVL 84

Expert Comment

by:ozo
ID: 39949626
Can you find an Omega(lg n) depth network for the first minimum?
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LVL 10

Author Comment

by:aboo_s
ID: 39949645
Yes, that's what I have found.  Attached is an example for N=8.
first-min.jpg
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Expert Comment

by:ozo
ID: 39949655
And does TommySzalapski's hint suggest a way to modify that yo find the second and third minimum?
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LVL 10

Author Comment

by:aboo_s
ID: 39949659
No, he only pointed out that if you can do it for the first it's no problem to do the second and third. But that wasn't what I asked. I asked to do it for the minimum in the first place.

Anyway, thank you all for your time, points will be split.
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Author Closing Comment

by:aboo_s
ID: 39949660
Thanks again.
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