On the Computational Complexity of MapReduce

TL;DR

This paper explores the computational complexity of MapReduce models, establishing their relation to classical complexity classes and demonstrating how additional rounds or time increase computational power.

Contribution

It introduces a uniform MRC model, connects MapReduce to regular languages and sublogarithmic space, and shows hierarchies based on rounds and time under complexity assumptions.

Findings

Regular languages are in constant round MRC.

Increasing rounds or time enhances MRC computational power.

First complexity-theoretic analysis of MapReduce models.

Abstract

In this paper we study MapReduce computations from a complexity-theoretic perspective. First, we formulate a uniform version of the MRC model of Karloff et al. (2010). We then show that the class of regular languages, and moreover all of sublogarithmic space, lies in constant round MRC. This result also applies to the MPC model of Andoni et al. (2014). In addition, we prove that, conditioned on a variant of the Exponential Time Hypothesis, there are strict hierarchies within MRC so that increasing the number of rounds or the amount of time per processor increases the power of MRC. To the best of our knowledge we are the first to approach the MapReduce model with complexity-theoretic techniques, and our work lays the foundation for further analysis relating MapReduce to established complexity classes.