LogP: a practical model of parallel computation
Communications of the ACM
Predicting the Running Times of Parallel Programs by Simulation
IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
On designing optimal parallel triangular solvers
Information and Computation
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Working within the LogP model, we present parallel triangular solvers which use forward/backward substitution and show that they are optimal. We begin by deriving several lower bounds on execution time for solving triangular linear systems. Specifically, we derive lower bounds in which it is assumed that the number of data items per processor is bounded, a general lower bound, and lower bounds for specific data layouts commonly used for this problem. Furthermore, algorithms are provided which have running times within a constant factor of the lower bounds described. One interesting result is that the popular 2-dimensional block matrix layout necessarily results in significantly longer running times than simpler one-dimensional schemes. Finally, we present a generalization of the lower bounds to banded triangular linear systems.