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Multiple sequence alignment is the most common task in computational biology. This multiple sequence alignment is computationally difficult and classified as a NP-Hard problem; so approximate algorithm(s) are generally required for most multiple alignment tasks. The Molecular Biologist may require the alignment of thousands of sequences that each can be of many hundreds of amino acids or even several millions of nucleotides. The approximation algorithm requires a long processing period of time to compute near optimal alignment. Thus, one step to reduce the processing time is to parallelize the algorithm. In order to have solution over parallelism method, we can either use expensive multiprocessor programming or cheaper cluster/Grid programming. Multiprocessor systems are specialized expensive hardware and are not commonly available. An alternative cheapest way is to use either a computer cluster or a Computing Grid. A cluster can be used for amino acid sequences and will be very slow for multiple sequence alignment of DNA molecule. So, the computing grid is the only cheapest alternative for performing multiple sequence alignment of DNA molecules. We have designed an efficient grid scheduler to perform the parallel tasks in grid that minimizes the communication cost and time complexity and also implemented parallel algorithm on computing grid. The experimental results show enhanced speedup.