On the parallel complexity of solving recurrence equations
We show that recurrence equations, even the simple ones, are not likely to admit fast parallel algorithms, i.e., not likely to be solvable in polylogarithmic time using a polynomial number of processors. We also look at a restricted class of recurrence equations and show that this class is solvable in O(log2n) time, but not likely in O(log n) time.
KeywordsParallel Algorithm Turing Machine Recurrence Equation Short Path Problem Polynomial Number
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- [HU79]J. Hopcroft and J. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, Mass., 1979.Google Scholar
- [Iba91]O. H. Ibarra. On resetting DLBA's. SIGACT News, 22(1):62–63, 1991.Google Scholar
- [IPS90]O. H. Ibarra, T-C. Pong, and S. M. Sohn. String processing on the hypercube. IEEE Trans. on Acoustics, Speech, and Signal Processing, 38:160–164, 1990.Google Scholar
- [IWJ93]O. H. Ibarra, H. Wang, and T. Jiang. On efficient parallel algorithms for solving set recurrence equations. Journal of Algorithms, 14(2):244–257, 1993.Google Scholar
- [Jaj92]J. Jaja. An Introduction to Parallel Algorithms. Addison-Wesley, Reading, Mass., 1992.Google Scholar
- [LN82]J. Van Leeuwen and M. Nivat. Efficient recognition of rational relations. Information Processing Letter, 14:34–38, 1982.Google Scholar
- [RS90]S. Ranka and S. Sahni. String editing on an SIMD hypercube multicomputer. Journal of Parallel and Distributed Computing, 9(4):411–418, 1990.Google Scholar
- [UG88]J. Ullman and A. Van Gelder. Parallel complexity of logical query programs. Algorithmic, 3:5–42, 1988.Google Scholar