# Communication vs Distributed Computation: an alternative trade-off curve

## TL;DR

This paper explores the trade-off between communication and distributed computation in MapReduce-like systems, considering storage constraints and computational limits, and proposes bounds and heuristics for optimizing this balance.

## Contribution

It introduces a new perspective on the communication-computation trade-off by accounting for partial computation and computational constraints, extending prior models.

## Key findings

- Derived lower bounds on communication load under computational constraints
- Proposed heuristic schemes that approach the theoretical bounds
- Highlighted the impact of partial computation on storage and communication trade-offs

## Abstract

In this paper, we revisit the communication vs. distributed computing trade-off, studied within the framework of MapReduce in [1]. An implicit assumption in the aforementioned work is that each server performs all possible computations on all the files stored in its memory. Our starting observation is that, if servers can compute only the intermediate values they need, then storage constraints do not directly imply computation constraints. We examine how this affects the communication-computation trade-off and suggest that the trade-off be studied with a predetermined storage constraint. We then proceed to examine the case where servers need to perform computationally intensive tasks, and may not have sufficient time to perform all computations required by the scheme in [1]. Given a threshold that limits the computational load, we derive a lower bound on the associated communication load, and propose a heuristic scheme that achieves in some cases the lower bound.