Recently, the predicate detection problem was shown to be in the parallel complexity class NC . In this paper, we give some more work efficient parallel algorithms 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, had work complexity O(m^3n^3\log mn). We give two algorithms, a deterministic algorithm with  work complexity O( m^2n^2) and a randomized algorithm with  work complexity O( m^2n^2). Furthermore, our algorithms have a space complexity of \textit{  O(mn^2) whereas ParallelCut had a space complexity of \textit{  O(m^2n^2).
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^3\log 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) work complexity O( mn^2). \% and two offline algorithms. The online deterministic algorithm has. Furthermore, our algorithms improve upon the space complexity of \textit{ParallelCut . Both of our algorithms have space complexity O(mn^2) whereas \textit{ParallelCut has space complexity O(m^2n^2).
R
NC
NC
R
some more work efficient parallel algorithms
the first work-optimal parallel algorithm
R
ParallelCut, had
ParallelCut
A
, has time complexity O(\log mn) and
A
time complexity O(mn) and
R
m^2n^2)
mn^2),
A
time complexity (mn)^{1/2 + o(1)
R
m^2n^2).
mn^2). \% and two offline algorithms. The online deterministic algorithm has.
R
have a
improve upon the
A
ParallelCut
A
. Both of our algorithms have space complexity
D
ParallelCut had a space complexity of
A
ParallelCut
A
has space complexity