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A general technique that can be used to solve a wide variety of discrete optimization problems is the branch-and-bound algorithm. We have adapted and extended branch-and-bound algorithms for parallel processing. The computational efficiency of these algorithms depends on the allowance function, the data structure, and the search strategies. Anomalies owing to parallelism may occur. In this correspondence, anomalies of parallel branch-and-bound algorithms using the same search strategy as the corresponding serial algorithms are studied. Sufficient conditions to guarantee no degradation in performance due to parallelism and necessary conditions for allowing parallelism to have a speedup greater than the number of processors are presented.