A Lower Bound Technique for Communication in BSP

TL;DR

This paper introduces a new lower bound technique for communication complexity in the BSP model, based on the switching potential of DAGs, applicable to FFT, sorting networks, and other models.

Contribution

It presents a novel method linking DAG switching potential to communication bounds, providing tight bounds for FFT and sorting networks, and extending to other computational models.

Findings

Tight lower bounds for FFT and sorting networks.

The switching potential effectively captures communication requirements.

The technique applies to models beyond BSP, like I/O and LPRAM.

Abstract

Communication is a major factor determining the performance of algorithms on current computing systems; it is therefore valuable to provide tight lower bounds on the communication complexity of computations. This paper presents a lower bound technique for the communication complexity in the bulk-synchronous parallel (BSP) model of a given class of DAG computations. The derived bound is expressed in terms of the switching potential of a DAG, that is, the number of permutations that the DAG can realize when viewed as a switching network. The proposed technique yields tight lower bounds for the fast Fourier transform (FFT), and for any sorting and permutation network. A stronger bound is also derived for the periodic balanced sorting network, by applying this technique to suitable subnetworks. Finally, we demonstrate that the switching potential captures communication requirements even in computational models different from BSP, such as the I/O model and the LPRAM.