On the Complexity of List Ranking in the Parallel External Memory Model

TL;DR

This paper investigates the computational complexity of list ranking in the parallel external memory model, establishing lower bounds and presenting an efficient algorithm, thereby advancing understanding of the problem's difficulty in parallel external memory systems.

Contribution

It proves a permuting lower bound in the PEM model and introduces a stronger 1og^2 N lower bound for a specific variant, along with an improved algorithm for certain parameters.

Findings

Established a permuting lower bound in PEM.

Proved a 1og^2 N lower bound for a special case.

Presented a tight algorithm for a broader parameter range.

Abstract

We study the problem of list ranking in the parallel external memory (PEM) model. We observe an interesting dual nature for the hardness of the problem due to limited information exchange among the processors about the structure of the list, on the one hand, and its close relationship to the problem of permuting data, which is known to be hard for the external memory models, on the other hand. By carefully defining the power of the computational model, we prove a permuting lower bound in the PEM model. Furthermore, we present a stronger \Omega(log^2 N) lower bound for a special variant of the problem and for a specific range of the model parameters, which takes us a step closer toward proving a non-trivial lower bound for the list ranking problem in the bulk-synchronous parallel (BSP) and MapReduce models. Finally, we also present an algorithm that is tight for a larger range of parameters of the model than in prior work.