Separating the power of EREW and CREW PRAMs with small communication width
We prove that evaluating a Boolean decision tree of height h requires Ω(h/log*h) time on any EREW PRAM with communication width one. Since this function can be easily solved in time O(√h) on a CREW PRAM with communication width one, this gives a separation between the two models. Our result can be extended to show a separation whenever the EREW PRAM has communication width m ε o(√h).
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- [Bea86]P. Beame. Lower Bounds in Parallel Machine Computation. PhD thesis, Department of Computer Science, University of Toronto, 1986. Also appears as Technical Report TR 198/87.Google Scholar
- [DKR90]M. Dietzfelbinger, M. Kutylowski, and R. Reischuk. Exact time bounds for computing Boolean functions on PRAMs without simultaneous writes. In Proceedings of the 1990 ACM Symposium on Parallel Algorithms and Architectures, pages 125–135, Crete, Greece, June 1990.Google Scholar
- [Sni85]M. Snir. On parallel searching. SIAM Journal on Computing, 14:688–708, 1985.Google Scholar
- [VW85]U. Vishkin and A. Wigderson. Trade-offs between depth and width in parallel computation. SIAM Journal on Computing, 14(2):303–314, May 1985.Google Scholar