Fast and Work-Optimal Parallel Algorithms for Predicate Detection
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Recently, the predicate detection problem was shown to be in the parallel complexity class NC. In this paper, we give the first work-optimal parallel algorithm to solve the predicate detection problem on a distributed computation with n processes and at most m states per process. The previous best known parallel predicate detection algorithm, ParallelCut, has time complexity O(log mn) and work complexity O(m^3n^3log mn). We give two algorithms, a deterministic algorithm with time complexity O(mn) and work complexity O(mn^2), and a randomized algorithm with time complexity (mn)^1/2 + o(1) and work complexity Õ(mn^2). Furthermore, our algorithms improve upon the space complexity of ParallelCut. Both of our algorithms have space complexity O(mn^2) whereas ParallelCut has space complexity O(m^2n^2).
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