TRADE-OFFS BETWEEN DEPTH AND WIDTH IN PARALLEL COMPUTATION.

A new technique for proving lower bounds for parallel computation is introduced. This technique enables the authors to obtain, for the first time, nontrivial tight lower bounds for shared-memory models of parallel computation that allow several processors to have simultaneous access to the same memory location. Specifically, they use a concurrent-read concurrent-write model of parallel computation. It has p processors, each has access to a common memory of size m (also called communication width or width in short). The input to the problem is located in an additional read-only portion of the common memory. For a wide variety of problems (including parity, majority and summation) they show that the time complexity T (depth) and the communication width m are related by the trade-off curve mT**2 equals OMEGA (n), (where n is the size of the input), regardless of the number of processors.