Efficient low-contention parallel algorithms

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 hypercube-type noncombining 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 experiment demonstrates the performance advantage of a new QRQW random permutation algorithm when compared with the popular EREW algorithm. Finally, this paper presents new randomized algorithms for integer sorting and general sorting.