No abstract

A vast body of theoretical research has focused either on overly simplistic models of parallel computation, notably the PRAM, or overly specific models that have few representatives in the real world. Both kinds of models encourage exploitation of formal loopholes, rather than rewarding development of techniques that yield performance across a range of current and future parallel machines. This paper offers a new parallel machine model, called LogP, that reflects the critical technology trends underlying parallel computers. it is intended to serve as a basis for developing fast, portable parallel algorithms and to offer guidelines to machine designers. Such a model must strike a balance between detail and simplicity in order to reveal important bottlenecks without making analysis of interesting problems intractable. The model is based on four parameters that specify abstractly the computing bandwidth, the communication bandwidth, the communication delay, and the efficiency of coupling communication and computation. Portable parallel algorithms typically adapt to the machine configuration, in terms of these parameters. The utility of the model is demonstrated through examples that are implemented on the CM-5.

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In many distributed-memory parallel computers the only built-in communication primitive is point-to-point message transmission, and more powerful operations such as broa&ast and synchronization must be realized using this primitive. Whhin the LogP model of parallel computation we present algorithms that yield optimal communication schedules for several broadcast and synchronization operations. Most of our algorithms arc the absolutely best possible in that not even the constant factors can be improved upon. For one particular broadcast problem, called continuous broadcast, the optimality of our algorithm is not yet completely proven, althoughproofs have been achieved for a certain range of pararnetem. We also devise an optimal algorithm for summin g or, more generally, applying a non~ommumtive associative binary operator to a set of operands.