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Upper Bounds on Number of Steals in Rooted Trees

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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 \({\sum }_{i=1}^{n}(k-1)^{i}\binom {h}{i}\).

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References

  1. Agrawal, K., He, Y., Leiserson, C.E.: An empirical evaluation of work stealing with parallelism feedback. In 26th IEEE International Conference on Distributed Computing Systems (ICDCS 2006) (2006)

  2. Arora, N.S., Blumofe, R.D., Greg Plaxton, C.: Thread scheduling for multiprogrammed multiprocessors. In: Proceedings of the Tenth Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 119–129 (1998)

  3. Blumofe, R.D., Leiserson, C.E.: Scheduling multithreaded computations by work stealing. J. ACM 46(5), 720–748 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  4. Warren Burton, F., Ronan Sleep, M.: Executing functional programs on a virtual tree of processors. In: Proceedings of the 1981 Conference on Functional Programming Languages and Computer Architecture, 187–194 (1981)

  5. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to algorithms, 3rd edition. The MIT Press (2009)

  6. Dinan, J., Larkins, D.B., Sadayappan, P., Krishnamoorthy, S., Nieplocha, J.: Scalable work stealing. In Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis (SC) (2009)

  7. Halstead Jr., R.H.: Implementation of Multilisp: Lisp on a multiprocessor. In: Proceedings of the 1984 ACM Symposium on LISP and Functional Programming, p. 9–17 (1984)

  8. Karp, R.M., Zhang, Y.: Randomized parallel algorithms for backtrack search and branch-and-bound computation. J. ACM 40(3), 765–789 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  9. Suksompong, W.: Bounds on multithreaded computations by work stealing. Master’s Thesis, Massachusetts Institute of Technology (2014)

  10. Tomizawa, N.: On some techniques useful for solution of transportation network problems. Networks 1(2), 1972

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Acknowledgments

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

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Authors and Affiliations

  1. MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St, Cambridge, MA, 02139, USA

    Charles E. Leiserson & Tao B. Schardl

  2. Department of Computer Science, Stanford University, 353 Serra Mall, Stanford, CA, 94305, USA

    Warut Suksompong

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  1. Charles E. Leiserson
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  2. Tao B. Schardl
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  3. Warut Suksompong
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Correspondence to Warut Suksompong.

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Leiserson, C.E., Schardl, T.B. & Suksompong, W. Upper Bounds on Number of Steals in Rooted Trees. Theory Comput Syst 58, 223–240 (2016). https://doi.org/10.1007/s00224-015-9613-9

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  • DOI: https://doi.org/10.1007/s00224-015-9613-9

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