Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
Separating the polynomial-time hierarchy by oracles
Proc. 26th annual symposium on Foundations of computer science
Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Upper and lower time bounds for parallel random access machines without simultaneous writes
SIAM Journal on Computing
Sorting in c log n parallel steps
Combinatorica
Bounds on the time for parallel RAM's to compute simple functions
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Parallelism in random access machines
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Timing for Associative Operations on the MASC Model
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
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The ability of the strongest parallel random access machine model WRAM is investigated. In this model different processors may simultaneously try to write into the same cell of the common memory. It has been shown that a parallel RAM without this option (PRAM), even with arbitrarily many processors, can almost never achieve sublogarithmic time. On the contrary, every function with a small domain like binary values in case of Boolean functions can be computed by a WRAM in constant time. The machine makes fast table look-ups using its simultaneous write ability. The main result of this paper implies that in general this is the “only way” to perform such fast computations and that a domain of small size is necessary. Otherwise simultaneous writes do not give an advantage. Functions with large domains for which any change of one of the n arguments also changes the result are considered, and a logarithmic lower time bound for WRAMs is proved. This bound can be achieved by machines that do not perform simultaneous writes. A simple example of such a function is the sum of n natural numbers.