Optimal Coding Scheme and Resource Allocation for Distributed Computation with Limited Resources

TL;DR

This paper develops an optimal resource allocation and coding scheme for distributed computing systems with limited resources, improving execution time by combining and extending existing CDC and ACDC approaches.

Contribution

It introduces a hybrid coding scheme that outperforms existing CDC and ACDC methods and proves its optimality under certain conditions through information-theoretic analysis.

Findings

Hybrid scheme outperforms CDC and ACDC.

Optimality proven for specific system parameters.

Resource allocation strategies minimize execution time.

Abstract

A central issue of distributed computing systems is how to optimally allocate computing and storage resources and design data shuffling strategies such that the total execution time for computing and data shuffling is minimized. This is extremely critical when the computation, storage and communication resources are limited. In this paper, we study the resource allocation and coding scheme for the MapReduce-type framework with limited resources. In particular, we focus on the coded distributed computing (CDC) approach proposed by Li et al.. We first extend the asymmetric CDC (ACDC) scheme proposed by Yu et al. to the cascade case where each output function is computed by multiple servers. Then we demonstrate that whether CDC or ACDC is better depends on system parameters (e.g., number of computing servers) and task parameters (e.g., number of input files), implying that neither CDC nor ACDC is optimal. By merging the ideas of CDC and ACDC, we propose a hybrid scheme and show that it can strictly outperform CDC and ACDC. Furthermore, we derive an information-theoretic converse showing that for the MapReduce task using a type of weakly symmetric Reduce assignment, which includes the Reduce assignments of CDC and ACDC as special cases, the hybrid scheme with a corresponding resource allocation strategy is optimal, i.e., achieves the minimum execution time, for an arbitrary amount of computing servers and storage memories.