Computational bounds for fundamental problems on general-purpose parallel models

Philip D. MacKenzie, Vijaya Ramachandran
1998 Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures - SPAA '98  
We present lower bounds for time needed to solve basic problems on three general-purpose models of parallel computation: the shared-memory models qsm and s-qsm, and the distributed-memory model, the bsp. For each of these models, we also obtain lower bounds for the number of rounds needed to solve these problems using a randomized algorithm on a p-processor machine. Our results on'rounds' is of special interest in the context of designing work-e cient algorithms on a machine where latency and
more » ... nchronization costs are high. Many of our lower bound results are complemented by upper bounds that match the lower bound or are close to it. Tracev; t; f 1 is the same as Tracev; t; f 2 . Intuitively, v is not dependent on inputs outside Knowv;t;G, since these could not a ect its trace, and v is dependent on every input inside Knowv;t;G by the fact that it is the minimum set of inputs which could a ect its trace. Let A Proci; t; G contain each processor p in which i 2 Knowp; t; G. Let A Celli; t; G contain each cell c in which i 2 Knowc; t; G. 23
doi:10.1145/277651.277681 dblp:conf/spaa/MackenzieR98 fatcat:zf2bjy3dajexnbymse7234i6c4