An Optimal Selection Algorithm

Cover An Optimal Selection Algorithm
An Optimal Selection Algorithm
Richard Cole
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This presentation has two advantages. First it provides for a comparison 'at a glance' with the best sequential algorithm. Second, it may make the description of the algorithm simpler: at times it is convenient to describe the algorithm as if different numbers of processors are being used for different steps of the algorithm, and simply to count the number of operations performed. We are assured, by Brent's theorem [B-74], that it is straightforward to simulate such an algorithm by a uniform nu...mber of processors. We remark that Brent's theorem ignores the following implementation issue: how to assign operations to processors. But for the algorithm given here this will present no difficulty. The details will be left to the reader.
We give an EREW PRAM algorithm for selection that uses 0{n) operations and 0{\ogn\og'n) time; it assumes that the input is provided in an array of length n. The algorithm makes use of the [AKS-83] sorting network. However, if the algorithm is implemented on a CREW PRAM we do not need to use this sorting We apply the reduction procedure recursively to obtain the approximation; let e be the item selected.


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