A Combinatorial Design for Cascaded Coded Distributed Computing on General Networks

TL;DR

This paper introduces a new combinatorial design for cascaded coded distributed computing that reduces communication load, requires fewer files and functions, and adapts well to heterogeneous networks, outperforming existing schemes.

Contribution

It proposes a low-complexity combinatorial scheme for cascaded CDC that optimally assigns files and functions, improving performance in both homogeneous and heterogeneous networks.

Findings

Outperforms state-of-the-art schemes in homogeneous networks.

Effective in heterogeneous networks with better performance than homogeneous schemes.

Achieves near-optimal performance within a constant factor of theoretical bounds.

Abstract

Coding theoretic approached have been developed to significantly reduce the communication load in modern distributed computing system. In particular, coded distributed computing (CDC) introduced by Li et al. can efficiently trade computation resources to reduce the communication load in MapReduce like computing systems. For the more general cascaded CDC, Map computations are repeated at r nodes to significantly reduce the communication load among nodes tasked with computing Q Reduce functions s times. In this paper, we propose a novel low-complexity combinatorial design for cascaded CDC which 1) determines both input file and output function assignments, 2) requires significantly less number of input files and output functions, and 3) operates on heterogeneous networks where nodes have varying storage and computing capabilities. We provide an analytical characterization of the computation-communication tradeoff, from which we show the proposed scheme can outperform the state-of-the-art scheme proposed by Li et al. for the homogeneous networks. Further, when the network is heterogeneous, we show that the performance of the proposed scheme can be better than its homogeneous counterpart. In addition, the proposed scheme is optimal within a constant factor of the information theoretic converse bound while fixing the input file and the output function assignments.