Analysis of Work-Stealing and Parallel Cache Complexity

TL;DR

This paper simplifies the analysis of the randomized work-stealing scheduler for educational purposes and introduces new parallel cache complexity bounds that improve upon previous results, especially for high-span algorithms.

Contribution

It provides an easy-to-understand analysis of the RWS scheduler and establishes new parallel cache complexity bounds decoupled from span, advancing theoretical understanding.

Findings

Simplified analysis of RWS scheduler without potential functions

New parallel cache bounds that are near optimal

Improved bounds for classic algorithms in parallel cache complexity

Abstract

Parallelism has become extremely popular over the past decade, and there have been a lot of new parallel algorithms and software. The randomized work-stealing (RWS) scheduler plays a crucial role in this ecosystem. In this paper, we study two important topics related to the randomized work-stealing scheduler. Our first contribution is a simplified, classroom-ready version of analysis for the RWS scheduler. The theoretical efficiency of the RWS scheduler has been analyzed for a variety of settings, but most of them are quite complicated. In this paper, we show a new analysis, which we believe is easy to understand, and can be especially useful in education. We avoid using the potential function in the analysis, and we assume a highly asynchronous setting, which is more realistic for today's parallel machines. Our second and main contribution is some new parallel cache complexity for algorithms using the RWS scheduler. Although the sequential I/O model has been well-studied over the past decades, so far very few results have extended it to the parallel setting. The parallel cache bounds of many existing algorithms are affected by a polynomial of the span, which causes a significant overhead for high-span algorithms. Our new analysis decouples the span from the analysis of the parallel cache complexity. This allows us to show new parallel cache bounds for a list of classic algorithms. Our results are only a polylogarithmic factor off the lower bounds, and significantly improve previous results.