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Theory of Computing Systems

, Volume 58, Issue 2, pp 223–240 | Cite as

Upper Bounds on Number of Steals in Rooted Trees

  • Charles E. Leiserson
  • Tao B. Schardl
  • Warut SuksompongEmail author
Article

Abstract

Inspired by applications in parallel computing, we analyze the setting of work stealing in multithreaded computations. We obtain tight upper bounds on the number of steals when the computation can be modeled by rooted trees. In particular, we show that if the computation with n processors starts with one processor having a complete k-ary tree of height h (and the remaining n − 1 processors having nothing), the maximum possible number of steals is \({\sum }_{i=1}^{n}(k-1)^{i}\binom {h}{i}\).

Keywords

Work stealing Parallel algorithm Extremal combinatorics Binomial coefficient 

Notes

Acknowledgments

We would like to thank the anonymous reviewers for their helpful feedback.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Charles E. Leiserson
    • 1
  • Tao B. Schardl
    • 1
  • Warut Suksompong
    • 2
    Email author
  1. 1.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  2. 2.Department of Computer ScienceStanford UniversityStanfordUSA

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