On the efficiency of localized work stealing

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 ∞ P ) , and that under the “even distribution of free agents assumption”, the expected running time of the algorithm is T 1 / P + O ( T ∞ 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 ∞ M ) .