Space-Efficient Parallel Algorithms for the Constrained Multiple Sequence Alignment Problem

Given sequences S1, S2, . . . Sn, and a pattern string P the constrained multiple sequence alignment problem (CMSA) is to align similar subsequences of these sequences with the constraint that the alignment “contains” P . The CMSA problem can be considered as an optimal path search problem in the dynamic programming matrix. The problem has a dynamic programming solution that requires O(2|S1||S2|...|Sn||P |) time and O(|S1||S2|...|Sn||P |) space where |S1|, |S2|, ..., |Sn| are the lengths of sequences S1, S2, ..., Sn, and |P | is the length of the pattern string, respectively. There is a parallel algorithm that uses |P | + 1 processors. The algorithm requires O(|S1||S2|...|Sn|) space for each processor. The memory requirement is a major bottleneck for the CMSA problem. In this paper, we propose two parallel algorithms which solve the CMSA problem and use less space on each processor than the ordinary dynamic programming algorithm and existing parallel algorithms for the problem.