Constant time BSR solutions to parenthesis matching, tree decoding, and tree reconstruction from its traversals

Recently Akl et al. introduced a new model of parallel computation, called BSR (broadcasting with selective reduction) and showed that it is more powerful than any CRCW PRAM and yet requires no more resources for implementation than even EREW PRAM. The model allows constant time solutions to sorting, parallel prefix and other problems. In this paper, we describe constant time solutions to the parenthesis matching, decoding binary trees in bitstring representation, generating next tree shape in B-order, and the reconstruction of binary trees from their traversals, using the BSR model. They are the first constant time solutions to mentioned problems on any model of computation. The number of processors used is equal to the input size, for each problem. A new algorithm for sorting integers is also presented.