A dominant point-based parallel algorithm that finds all longest common subsequences for a constrained-MLCS problem

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The work presented in this paper consists of searching for all the longest common subsequences among r sequences of equal length n which exclude a particular string. This problem is named the constrained-multiple longest common subsequence (constrained-MLCS) and is a general case of the constrained-LCS. Due to its importance, particularly in bioinformatics, the constrained-MLCS is widely studied. Thus, the solution proposed here is a coarse-grained multicomputer-based algorithm that uses an existing serial algorithm for local computation and a master-slave paradigm. This solution requires OD×Σ+ CSSs×MLCSp local computation time on each processor , OMLCS communication rounds and Onr|Σ|p time for preliminary works. |Σ| is the alphabet’s size, p is the number of processors used, |D| is the number of dominants generated during the entire resolution process, CSSs and MLCS are the number of all common subsequences, and the length of the longest common subsequences respectively. The experiments performed indicate that our proposed algorithm is scalable both with the number of processors and the number of input sequences.