An Improved Lower Bound for the QRQW PRAM

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. Here we present a lower bound for the problem of Linear Approximate Compaction (LAC) on the QRQW PRAM. The input to LAC consists of at most m marked items in an array of size n, and the output consists of the marked items in an array of size O(m). There is an O(p log n) expected time randomized algorithm for LAC on the QRQW PRAM. We prove a lower bound of (log log n) expected time for any randomized algorithm for LAC, an improvement over the previous best bound of (log log logn). Our bound applies regardless of the number of processors and memory cells of the QRQW PRAM.