  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 $T_1/P+O(T_\infty M)$.
