A Construction of Asymptotically Optimal Cascaded CDC Schemes via Combinatorial Designs

TL;DR

This paper introduces new asymptotically optimal cascaded CDC schemes using combinatorial 1-designs, reducing computation load and offering more flexible parameters while maintaining optimal communication load.

Contribution

The paper proposes novel asymptotically optimal cascaded CDC schemes based on 1-designs, improving computational efficiency and parameter flexibility over previous symmetric design-based schemes.

Findings

Reduced computation loads compared to earlier schemes

Maintained optimal communication load

Enhanced parameter flexibility in scheme design

Abstract

A coded distributed computing (CDC) system aims to reduce the communication load in the MapReduce framework. Such a system has $K$ nodes, $N$ input files, and $Q$ Reduce functions. Each input file is mapped by $r$ nodes and each Reduce function is computed by $s$ nodes. The objective is to achieve the maximum multicast gain. There are known CDC schemes that achieve optimal communication load. In some prominent known schemes, however, $N$ and $Q$ grow too fast in terms of $K$, greatly reducing their gains in practical scenarios. To mitigate the situation, some asymptotically optimal cascaded CDC schemes with $r=s$ have been proposed by using symmetric designs. In this paper, we put forward new asymptotically optimal cascaded CDC schemes with $r=s$ by using $1$-designs. Compared with earlier schemes from symmetric designs, ours have much smaller computation loads while keeping the other relevant parameters the same. We also obtain new asymptotically optimal cascaded CDC schemes with more flexible parameters compared with previously best-performing schemes.