Computation-Aware Data Aggregation

TL;DR

This paper introduces a new distributed computation model that accounts for both computation and communication times, providing algorithms for optimal data aggregation schedules on complete and arbitrary graphs, and analyzing their complexity.

Contribution

It presents a novel model incorporating compute time into data aggregation, along with polynomial-time algorithms for complete graphs and approximation algorithms for arbitrary graphs.

Findings

Optimal schedule computation for complete graphs in polynomial time.

Data aggregation on arbitrary graphs is hard to approximate within 1.5.

An O(log n * log(OPT/t_m))-approximation algorithm for arbitrary graphs.

Abstract

Data aggregation is a fundamental primitive in distributed computing wherein a network computes a function of every nodes' input. However, while compute time is non-negligible in modern systems, standard models of distributed computing do not take compute time into account. Rather, most distributed models of computation only explicitly consider communication time. In this paper, we introduce a model of distributed computation that considers \emph{both} computation and communication so as to give a theoretical treatment of data aggregation. We study both the structure of and how to compute the fastest data aggregation schedule in this model. As our first result, we give a polynomial-time algorithm that computes the optimal schedule when the input network is a complete graph. Moreover, since one may want to aggregate data over a pre-existing network, we also study data aggregation scheduling on arbitrary graphs. We demonstrate that this problem on arbitrary graphs is hard to approximate within a multiplicative $1.5$ factor. Finally, we give an $O(\log n \cdot \log \frac{\mathrm{OPT}}{t_m})$-approximation algorithm for this problem on arbitrary graphs, where $n$ is the number of nodes and $\mathrm{OPT}$ is the length of the optimal schedule.