Trade Offs Between Depth And Width in Parallel Computation
Trade Offs Between Depth And Width in Parallel Computation
U Vishkin
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T. F {x)^f {y). This contradicts lemma 2. 2. Therefore 7'{ 7 + 1)/ 2 3^ /b, so r = n(V;G' ). • 2. 3. Lower Bounds for the CREW PRAM(l) Consider the OR function of n bits. As mentioned earlier, the OR is just 1- sensitive everywhere, so the results in the previous subsection imply only a con- stant time lower bound for it on the CRCW PRAM(l). Indeed, there is a two-step algorithm for the OR on this model as follows. In the first step, the common memory cell C is initialized with "O". In the seco...nd step, a processor Pi reads the ith input position and writes a '1' into C ifT the value it read was ' 1". It is clear why this edgorithm is not valid for a CREW PRAM. Note, however, that if the domain consists only of inputs which have at most one position con- taining a '1', a write conflict cannot occur, and the algorithm is valid for the CREW PRAM. For this reason we will restrict ourselves here to functions with a full domain (i. E. I=E"). The mean result in this subsection is: Theorem 2.
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