Lower bound for the QRQW PRAM

摘要

The queue-read, queue-write (QRQW) parallel random access machine (PRAM) model is a shared memory model which allows concurrent reading and writing with a time cost proportional to the contention. This is designed to model currently available parallel machines more accurately than either the CRCW PRAM or EREW PRAM models. Many algorithmic results have been developed for the QRQW PRAM. However, the only lower bound results have been fairly simple reductions from lower bounds for other models, such as the EREW PRAM or the ''few-write'' CREW PRAM. Here we present a lower bound specific to the QRQW PRAM. This lower bound is on the problem of Linear Approximate Compaction (LAC), whose input consists of at most m marked items in an array of size n, and whose output consists of the rn marked items in an array of size 0(m). There is an O((radical)log n), expected time randomized algorithm for LAC on the QRQW PRAM. We prove a lower bound of (Omega)(log log log n) expected time for any randomized algorithm for LAC. This bound applies regardless of the number of processors and memory cells of the QRQW PRAM. The previous best lower bound was (Omega)(log* n) time, taken from the known lower bound for LAC on the CRCW PRAM.