The spatial computer: A model for energy-efficient parallel computation

TL;DR

This paper introduces a spatial computation model emphasizing energy efficiency based on processor distances, providing bounds for fundamental problems and methods to simulate traditional algorithms within this framework.

Contribution

The paper presents a novel spatial computation model with energy-aware communication costs and establishes bounds for key problems, simplifying analysis and extending to more complex models.

Findings

Established energy bounds for sorting, median selection, and matrix multiplication.

Demonstrated simulation of PRAM algorithms within the spatial model.

Extended the model to include local memory size as a parameter.

Abstract

We present a new parallel model of computation suitable for spatial architectures, for which the energy used for communication heavily depends on the distance of the communicating processors. In our model, processors have locations on a conceptual two-dimensional grid, and their distance therein determines their communication cost. In particular, we introduce the energy cost of a spatial computation, which measures the total distance traveled by all messages, and study the depth of communication, which measures the largest number of hops of a chain of messages. We show matching energy lower- and upper bounds for many foundational problems, including sorting, median selection, and matrix multiplication. Our model does not depend on any parameters other than the input shape and size, simplifying algorithm analysis. We also show how to simulate PRAM algorithms in our model and how to obtain results for a more complex model that introduces the size of the local memories of the processors as a parameter.