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A Probabilistic Pipeline Algorithm for K Selection on the Tree Machine

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2 Author(s)
Greenberg, A.G. ; Mathematics and Statistics Research Center, AT&T Bell Laboratories ; Manber, U.

We consider the problem of selecting the kth largest of n inputs, where initially the inputs are stored in the n leaf processors of the 2n − 1 processor tree machine. A probabilistic algorithm is presented that implements a type of pipelining to solve the problem in a simple data driven fashion, with each processor maintaining just a constant amount of state information. On any problem instance, the algorithm's running time is <c [log2n]/[loglog n], for some constant c > 0, with overwhelming probability.

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Computers, IEEE Transactions on  (Volume:C-36 ,  Issue: 3 )