Communication Lower Bounds for Distributed-Memory Computations∗
Michele Scquizzato, Francesco Silvestri · 2015
In this paper we propose a new approach to the study of the communication requirements of distributed computations, which advocates for the removal of the restrictive assumptions under which earlier results were derived. We illustrate our approach by giving tight lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, compar-ison sorting, and the Fast Fourier Transform. Our bounds rely only on a mild assumption on work distribution, and significantly strengthen previous results which require either the compu-tation to be balanced among the processors, or specific initial distributions of the input data, or an upper bound on the size of processors ’ local memories.