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Very fast optimal parallel algorithms for heap construction

Author: Paul Frederick Dietz; Rajeev Raman
Publisher: College Park, Md. : University of Maryland, [1994]
Series: Computer science technical report series (University of Maryland at College Park), CS-TR-3332.
Edition/Format:   Book : English
Database:WorldCat
Summary:
Abstract: "We give two algorithms for permuting n items in an array into heap order on a CRCW PRAM. The first is deterministic and runs in O(loglogn) time and performs O(n) operations. This run-time is the best possible for any comparison-based algorithm using n processors. The second is randomized and runs in O(logloglog n) time with high probability, performing O(n) operations. No PRAM algorithm with o(log n)  Read more...
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Document Type: Book
All Authors / Contributors: Paul Frederick Dietz; Rajeev Raman
OCLC Number: 31961352
Notes: "UMIACS-TR-94-98"--Cover.
"July 19, 1994."
Description: 15 p. ; 28 cm.
Series Title: Computer science technical report series (University of Maryland at College Park), CS-TR-3332.
Responsibility: Paul F. Dietz, Rajeev Raman.

Abstract:

Abstract: "We give two algorithms for permuting n items in an array into heap order on a CRCW PRAM. The first is deterministic and runs in O(loglogn) time and performs O(n) operations. This run-time is the best possible for any comparison-based algorithm using n processors. The second is randomized and runs in O(logloglog n) time with high probability, performing O(n) operations. No PRAM algorithm with o(log n) run-time was previously known for this problem. In order to obtain the deterministic result we study the parallel complexity of selecting the kth smallest of n elements on the CRCW PRAM, a problem that is of independent interest. We give an algorithm that is superior to existing ones when k is small compared to n. Consequently, we show that this problem can be solved in O(loglog n + log k/loglog n) time and O(n) operations for all 1 [<or =] k [<or =] n/2. A matching time lower bound is shown for all algorithms that use n or fewer processors to solve this problem."

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