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In this paper, a new data structure called string-queue is proposed in order to implement more efficiently the selection rule and the elimination rule of the general branch-and-bound algorithm. A new general parallel branch-and-bound algorithm on a distributed memory multiprocessor system is also presented. Its communication complexity in single iteration is down to its lower bound O(p) on a 2D mesh network. Both theoretical analysis and experimental results show that its average computational complexity is nearly in its lower bound.