Quickselect is a version of Quicksort that makes it possible to find efficiently any element in an unsorted file given its rank. ``Multiple Quickselect'' is designed to find simultaneously a collection of elements, also specified by their ranks. This talk shows how to analyse Multiple Quickselect when the underlying permutation is random and the collection of ranks is a random p-subset (p fixed). The analysis provides a nice illustration of the use of multivariate generating functions.
Pn,p= |
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P[n;j1,...,jp], |
Cn,p= |
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C[n;j1,...,jp] |
Pr{K=k}= |
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P n,p= | ( | Hn+1-Hp | ) |
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- |
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. (3) |
Pn,1=2 |
æ ç ç è |
1+ |
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ö ÷ ÷ ø |
Hn-3. |
Vn,p |
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Vn,1=-4 |
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Hn+12+ |
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Hn+1 -4 |
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Hn+1(2)+ |
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F'(z,u,v)=(1+u)F2(zv,u,v)+ |
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- |
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Cn,p =- |
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Hn+1 + |
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Hp + |
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Cn,1=3n-8 |
æ ç ç è |
1+ |
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ö ÷ ÷ ø |
Hn+13, Cn,n=2(n+1)Hn-4n. |
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