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DNA sequence assembly is one of the most popular problems in molecular biology. DNA sequence assembly refers to aligning and merging fragments of a much longer DNA sequence in order to reconstruct the original sequence. There are many solutions provided by researchers. In this paper we have adopted the features of the Particle Swarm Optimization (PSO) algorithm with Smallest Position Value (SPV) rule and designed a sequential algorithm to solve DNA sequence assembly and named it DSAPSO. DNA sequence assembly problem is a discrete optimization problem, so there is need of discrete optimization algorithm to solve it. We use continuous version of PSO with SPV rule to solve the DNA sequence assembly problem. SPV rule transforms continuous version of PSO to discrete version. To check the efficiency of proposed methodology the results of DSAPSO is compared with the results of genetic algorithm (GA).