TY - GEN

T1 - Converting high probability into nearly-constant time - with applications to parallel hashing

AU - Matias, Yossi

AU - Vishkin, Uzi

N1 - Publisher Copyright:
© 1991 ACM.

PY - 1991/1/3

Y1 - 1991/1/3

N2 - We present a new paradigm for efficient randomized parallel algorithms that needs ō(log' n) time, where Ō(x) means 'O(Z) expected'. It leads to: (1) constructing a perfect hash function for n elements in Ō (log" n log(log" n)) time and Ō (n) operations; (2) an algorithm for generating a random per-mutation in O(log∗ n) time, using n processors or in Ō (log" n Iog(log" n)) time and Ō (n) operations; and (3) an efficient optimize. consider a parallel algorithm that runs in t time using p processors; since at each time unit some of the processors may be idle, we let z, the total number of actual operations, be the sum over all non-idle processors at every time unit; assuming the algorithm belongs to a certain kind, it can be adapted to run in Ō (t+log" n log(log" n)) time (additive cwerhead!) using z/(t + log∗ n log(log∗ n)) processors. We ak get an optimal integer sorting adgorithm. Givel ntegers from the domain [1, .n], it runs in Ō( log/log n K ) time.

AB - We present a new paradigm for efficient randomized parallel algorithms that needs ō(log' n) time, where Ō(x) means 'O(Z) expected'. It leads to: (1) constructing a perfect hash function for n elements in Ō (log" n log(log" n)) time and Ō (n) operations; (2) an algorithm for generating a random per-mutation in O(log∗ n) time, using n processors or in Ō (log" n Iog(log" n)) time and Ō (n) operations; and (3) an efficient optimize. consider a parallel algorithm that runs in t time using p processors; since at each time unit some of the processors may be idle, we let z, the total number of actual operations, be the sum over all non-idle processors at every time unit; assuming the algorithm belongs to a certain kind, it can be adapted to run in Ō (t+log" n log(log" n)) time (additive cwerhead!) using z/(t + log∗ n log(log∗ n)) processors. We ak get an optimal integer sorting adgorithm. Givel ntegers from the domain [1, .n], it runs in Ō( log/log n K ) time.

UR - http://www.scopus.com/inward/record.url?scp=84983648984&partnerID=8YFLogxK

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AN - SCOPUS:84983648984

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 307

EP - 316

BT - Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991

PB - Association for Computing Machinery

T2 - 23rd Annual ACM Symposium on Theory of Computing, STOC 1991

Y2 - 5 May 1991 through 8 May 1991

ER -