EFFICIENT PARALLEL ALGORITHMS FOR THE LIS AND LCS PROBLEMS ON BSR MODEL USING CONSTANT NUMBER OF SELECTIONS

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 solution to the longest common subsequence (LCS) and longest increasing subsequence (LIS) problems using the BSR model. The number of processors used to solve the LCS problem is O(N × M) (where N and M are the length of the two input sequences). Our BSR solution of the LIS problem needs O(N) processors (where N is the length of the input sequence). These two solutions use BSR instructions with a constant number of selections. It is an improvement of our former BSR algorithm for the LCS in (Journal of Parallel and Distributed Computing, to appear) which uses 3N + 3 selections.