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Efficient LowContention Parallel Algorithms
 the 1994 ACM Symp. on Parallel Algorithms and Architectures
, 1994
"... The queueread, queuewrite (qrqw) parallel random access machine (pram) model permits concurrent reading and writing to shared memory locations, but at a cost proportional to the number of readers/writers to any one memory location in a given step. The qrqw pram model reflects the contention prope ..."
Abstract

Cited by 31 (12 self)
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The queueread, queuewrite (qrqw) parallel random access machine (pram) model permits concurrent reading and writing to shared memory locations, but at a cost proportional to the number of readers/writers to any one memory location in a given step. The qrqw pram model reflects the contention properties of most commercially available parallel machines more accurately than either the wellstudied crcw pram or erew pram models, and can be efficiently emulated with only logarithmic slowdown on hypercubetype noncombining networks. This paper describes fast, lowcontention, workoptimal, randomized qrqw pram algorithms for the fundamental problems of load balancing, multiple compaction, generating a random permutation, parallel hashing, and distributive sorting. These logarithmic or sublogarithmic time algorithms considerably improve upon the best known erew pram algorithms for these problems, while avoiding the highcontention steps typical of crcw pram algorithms. An illustrative expe...
The expected length of the longest probe sequence when the distribution is not uniform
 Journal of Algorithms
, 1985
"... We study the expected value of the maximum number of accesses needed to locate an element in a hashing file constructed by using an orderpreserving hashing function and with collision resolution by the method of separate chaining. It is assumed that X1,..., X „ are independent [0, 1]valued random ..."
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Cited by 7 (5 self)
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We study the expected value of the maximum number of accesses needed to locate an element in a hashing file constructed by using an orderpreserving hashing function and with collision resolution by the method of separate chaining. It is assumed that X1,..., X „ are independent [0, 1]valued random variables with common density f, and that XI is hashed to the nX; + 1st bucket (chain). For all densities that are bounded, the expected value of the maximum number of accesses is shown to be asymptotic to log n/log log n, and the dependency of this expected value on f is made explicit by exhibiting the first few terms in the asymptotic expansion. For unbounded f, a tight upper bound is given for the expected value. © 1985 Academic Press, Inc. 1