On the efficiency of localized work stealing

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[subscript 1]/P + O(T[subscript ∞]P), and that under the “even distribution of free agents assumption”, the expected running time of the algorithm is T[subscript 1]/P + O(T[subscript ∞]lgP) . 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[subscript 1]/ P+ O(T[subscript ∞]M). Keywords: Parallel algorithms; Multihreaded computation; Work stealing; Localizatio