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Sequence alignment algorithms such as the Smith-Waterman algorithm are among the most important applications in the development of bioinformatics. Sequence alignment algorithms must process large amounts of data which may take a long time. Here, we introduce our Adaptive Hybrid Multiprocessor technique to accelerate the implementation of the Smith-Waterman algorithm. Our technique utilizes both the graphics processing unit (GPU) and the central processing unit (CPU). It adapts to the implementation according to the number of CPUs given as input by efficiently distributing the workload between the processing units. Using existing resources (GPU and CPU) in an efficient way is a novel approach. The peak performance achieved for the platforms GPU + CPU, GPU + 2CPUs, and GPU + 3CPUs is 10.4 GCUPS, 13.7 GCUPS, and 18.6 GCUPS, respectively (with the query length of 511 amino acid).