Abstract
Samal and Henderson claim that any parallel algorithm for enforcing arc consistency in the worst case must have Ω(na) sequential steps, wheren is the number of nodes, anda is the number of labels per node. We argue that Samal and Henderson's argument makes assumptions about how processors are used and give a counterexample that enforces arc consistency in a constant number of steps usingO(n[su2a22na) processors. It is possible that the lower bound holds for a polynomial number of processors; if such a lower bound were to be proven it would answer an important open question in theoretical computer science concerning the relation between the complexity classesP andNC. The strongest existing lower bound for the arc consistency problem states that it cannot be solved in polynomial log time unlessP=NC.
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Swain, M.J. Comments on Samal and Henderson: “Parallel consistent labeling algorithms”. Int J Parallel Prog 17, 523–528 (1988). https://doi.org/10.1007/BF01407817
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DOI: https://doi.org/10.1007/BF01407817