Abstract. We define a natural and realistic model of parallel computation called the PRAM model without bit operations. It is like the usual PRAM model, the main di#erence being that no bit operations are provided. It encompasses virtually all known parallel algorithms for (weighted) combinatorial optimization and algebraic problems. In this model we prove that for some large enough constant b, the mincost-flow problem for graphs with n vertices cannot be solved deterministically (or with randomization) in # n/b (expected) time using 2 # n/b processors; this is so even if we restrict every cost and capacity to be an integer (nonnegative if it is a capacity) of bitlength at most an for some large enough constant a. A similar lower bound is also proved for the max-flow problem. It follows that these problems cannot be solved in our model deterministically (or with randomization)
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