The Influence of Placement on Transmission in Distributed Computing of Boolean Functions

TL;DR

This paper investigates how data placement affects transmission efficiency in distributed Boolean function computation, proposing a novel method to optimize placement and minimize communication costs based on Boolean function sensitivity.

Contribution

It introduces a new approach linking dataset placement and server transmission costs using Boolean function sensitivity, identifying optimal placement strategies.

Findings

Achieves minimum average joint sensitivity of N/2^{M-1} as a measure of communication cost.

Establishes a method to optimize dataset placement to reduce communication in distributed Boolean function computation.

Provides theoretical insights into the relationship between data placement, Boolean function properties, and communication efficiency.

Abstract

In this paper, we explore a distributed setting, where a user seeks to compute a linearly-separable Boolean function of degree $M$ from $N$ servers, each with a cache size $M$. Exploiting the fundamental concepts of sensitivity and influences of Boolean functions, we devise a novel approach to capture the interplay between dataset placement across servers and server transmissions and to determine the optimal solution for dataset placement that minimizes the communication cost. In particular, we showcase the achievability of the minimum average joint sensitivity, $\frac{N}{2^{M-1}}$, as a measure for the communication cost.