The queue-read, queue-write (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 well-studied crcw pram or erew pram models, and can be efficiently emulated with only logarithmic slowdown on hypercubetype non-combining networks. This paper describes fast, low-contention, work-optimal, 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 high-contention steps typical of crcw pram algorithms. An illustrative expe...

We study the expected value of the maximum number of accesses needed to locate an element in a hashing file constructed by using an order-preserving 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