## The natural work-stealing algorithm is stable (2001)

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Venue: | In Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science (FOCS |

Citations: | 26 - 1 self |

### BibTeX

@INPROCEEDINGS{Berenbrink01thenatural,

author = {Petra Berenbrink and Tom Friedetzky and Leslie Ann Goldberg},

title = {The natural work-stealing algorithm is stable},

booktitle = {In Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science (FOCS},

year = {2001},

pages = {178--187}

}

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### Abstract

In this paper we analyse a very simple dynamic work-stealing algorithm. In the workgeneration model, there are n (work) generators. A generator-allocation function is simply a function from the n generators to the n processors. We consider a fixed, but arbitrary, distribution D over generator-allocation functions. During each time-step of our process, a generator-allocation function h is chosen from D, and the generators are allocated to the processors according to h. Each generator may then generate a unit-time task which it inserts into the queue of its host processor. It generates such a task independently with probability λ. After the new tasks are generated, each processor removes one task from its queue and services it. For many choices of D, the work-generation model allows the load to become arbitrarily imbalanced, even when λ < 1. For example, D could be the point distribution containing a single function h which allocates all of the generators to just one processor. For this choice of D, the chosen processor receives around λn units of work at each step and services one. The natural work-stealing algorithm that we analyse is widely used in practical applications and works as follows. During each time step, each empty