Time optimal n-size matching parentheses and binary tree decoding algorithms on a p-processor BSR

Time optimal algorithms on an n-processor BSR PRAM for many n-size problems can be found in the literature. They outpace those on EREW, CREW or CRCW PRAM for the same problems. When only p (1 < p < n) processors are available, efficient algorithms on a p-processor BSR for some n-size problems can not be obtained from those on an n-processor BSR, and they have to be reconsidered. In this paper, we discuss and give two algorithms on a p-processor BSR for the two n-size problems of matching parentheses and decoding a binary tree from its bit-string, respectively, and show that they are time optimal.