On the Efficiency of Localized Work Stealing

TL;DR

This paper introduces a localized work-stealing algorithm with steal-back, analyzing its expected running time and demonstrating improved bounds under certain assumptions, emphasizing the benefits of locality in parallel task scheduling.

Contribution

The paper proposes a novel localized work-stealing variant with steal-back, providing theoretical analysis of its expected running time under various assumptions and task distributions.

Findings

Expected running time is T_1/P + O(T_∞ P)

Under even distribution, expected time improves to T_1/P + O(T_∞ log P)

Running time depends on task size ratios, bounded by T_1/P + O(T_∞ M)

Abstract

This paper investigates a variant of the work-stealing algorithm that we call the localized work-stealing algorithm. The intuition behind this variant is that because of locality, processors can benefit from working on their own work. Consequently, when a processor is free, it makes a steal attempt to get back its own work. We call this type of steal a steal-back. We show that the expected running time of the algorithm is $T_1/P+O(T_\infty P)$, and that under the "even distribution of free agents assumption", the expected running time of the algorithm is $T_1/P+O(T_\infty\lg P)$. In addition, we obtain another running-time bound based on ratios between the sizes of serial tasks in the computation. If $M$ denotes the maximum ratio between the largest and the smallest serial tasks of a processor after removing a total of $O(P)$ serial tasks across all processors from consideration, then the expected running time of the algorithm is $T_1/P+O(T_\infty M)$.