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We examine computational complexity implications for scheduling problems with job precedence relations with respect to strong precedence versus weak precedence. We propose a consistent definition of strong precedence for chains, trees, and series-parallel orders. Using modular decomposition for partially ordered sets (posets), we restate and extend past complexity results for chains and trees as summarized in Dror (1997) . Moreover, for series-parallel posets we establish new computationaldoi:10.1016/j.dam.2010.06.015 fatcat:lkdb4tkatzd6zphujfvqdshjy4