Abstract
We study the parallel complexity of selecting thekth smallest ofnelements on the CRCW PRAM. We show that this problem can be solved inO(log logn+ logk/log logn) time andO(n) operations for all 1?k?n/2, which is superior to existing deterministic bounds whenkis small compared ton. A matching time lower bound is shown for all algorithms that usenor fewer processors to solve this problem. As an application of the selection result, we give an algorithm for permutingnitems in an array into heap order on a CRCW PRAM inO(log logn) time andO(n) operations. By using randomization, the running time of this algorithm can be improved toO(log log logn) with high probability, still performingO(n) operations. No PRAM algorithm witho(logn) run time was previously known for this problem. We also obtain improved algorithms for constructingk-bandwidthheaps andmin-pathheaps.
Published Version
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