Skip to main content
SpringerLink
Log in

The scalability analysis of a parallel tree search algorithm

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

Increasing the number of computational cores is a primary way of achieving the high performance of contemporary supercomputers. However, developing parallel applications capable to harness the enormous amount of cores is a challenging task. It is very important to understand the principle limitations of the scalability of parallel applications imposed by the algorithm’s structure. The tree search addressed in this paper has an irregular structure unknown prior to computations. That is why such algorithms are challenging for parallel implementation especially on distributed memory systems. In this paper, we propose a parallel tree search algorithm aimed at distributed memory parallel computers. For this parallel algorithm, we analyze its scalability and show that it is close to the theoretical maximum.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Baldwin, A., Asaithambi, A.: An efficient method for parallel interval global optimization. In: 2011 International Conference on High Performance Computing and Simulation (HPCS), pp. 317–321. IEEE (2011)

  2. Barkalov, K., Gergel, V.: Parallel global optimization on gpu. J. Global Optim. 66(1), 3–20 (2016)

    Article  MathSciNet  Google Scholar 

  3. Bhatt, S., Greenberg, D., Leighton, T., Liu, P.: Tight bounds for on-line tree embeddings. SIAM J. Comput. 29(2), 474–491 (1999)

    Article  MathSciNet  Google Scholar 

  4. Casado, L.G., Martinez, J.A., García, I., Hendrix, E.M.T.: Branch-and-bound interval global optimization on shared memory multiprocessors. Optim. Methods Softw. 23(5), 689–701 (2008)

    Article  MathSciNet  Google Scholar 

  5. Evtushenko, Y., Posypkin, M., Rybak, L., Turkin, A.: Approximating a solution set of nonlinear inequalities. J. Global Optim. 71(1), 129–145 (2018)

    Article  MathSciNet  Google Scholar 

  6. Evtushenko, Y., Posypkin, M., Sigal, I.: A framework for parallel large-scale global optimization. Comput. Sci. Res. Dev. 23(3–4), 211–215 (2009)

    Article  Google Scholar 

  7. Gergel, V.P., Sergeyev, Y.D.: Sequential and parallel algorithms for global minimizing functions with lipschitzian derivatives. Comput. Math. Appl. 37(4–5), 163–179 (1999)

    Article  MathSciNet  Google Scholar 

  8. Gmys, J., Leroy, R., Mezmaz, M., Melab, N., Tuyttens, D.: Work stealing with private integer-vector-matrix data structure for multi-core branch-and-bound algorithms. Concurr. Comput. Pract. Exp. 28(18), 4463–4484 (2016)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  10. Knuth, D.E.: Estimating the efficiency of backtrack programs. Math. Comput. 29(129), 122–136 (1975)

    Article  MathSciNet  Google Scholar 

  11. Kolpakov, R., Posypkin, M.: The scalability analysis of a parallel tree search algorithm. In: Optimization and Applications. Proceedings of 9th International Conference OPTIMA 2018, Petrovac, Montenegro, October 1–5, 2018, pp. 186–201. Springer (2019)

  12. Kolpakov, R.M., Posypkin, M.A.: Upper and lower bounds for the complexity of the branch and bound method for the knapsack problem. Discrete Math. Appl. 20(1), 95–112 (2010)

    Article  MathSciNet  Google Scholar 

  13. Kolpakov, R.M., Posypkin, M.A.: Estimating the computational complexity of one variant of parallel realization of the branch-and-bound method for the knapsack problem. J. Comput. Syst. Sci. Int. 50(5), 756 (2011)

    Article  MathSciNet  Google Scholar 

  14. Kolpakov, R.M., Posypkin, M.A., Sigal, I.K.: On a lower bound on the computational complexity of a parallel implementation of the branch-and-bound method. Autom. Remote Control 71(10), 2152–2161 (2010)

    Article  MathSciNet  Google Scholar 

  15. Roucairol, C.: A parallel branch and bound algorithm for the quadratic assignment problem. Discrete Appl. Math. 18(2), 211–225 (1987)

    Article  MathSciNet  Google Scholar 

  16. Sergeyev, Y., Grishagin, V.: Parallel asynchronous global search and the nested optimization scheme. J. Comput. Anal. Appl. 3(2), 123–145 (2001)

    MathSciNet  MATH  Google Scholar 

  17. Sergeyev, Y.D., Grishagin, V.A.: Sequential and parallel algorithms for global optimization. Optim. Methods Softw. 3(1–3), 111–124 (1994)

    Article  Google Scholar 

  18. Strongin, R., Sergeyev, Y.: Global multidimensional optimization on parallel computer. Parallel Comput. 18(11), 1259–1273 (1992)

    Article  MathSciNet  Google Scholar 

  19. Strongin, R., Sergeyev, Y.: Global optimization: fractal approach and non-redundant parallelism. J. Global Optim. 27(1), 25–50 (2003)

    Article  MathSciNet  Google Scholar 

  20. Vu, T.T., Derbel, B.: Parallel branch-and-bound in multi-core multi-cpu multi-gpu heterogeneous environments. Future Gener. Comput. Syst. 56, 95–109 (2016)

    Article  Google Scholar 

  21. Wu, I.C., Kung, H.T.: Communication complexity for parallel divide-and-conquer. In: Proceedings 32nd Annual Symposium on Foundations of Computer Science, 1991, pp. 151–162. IEEE (1991)

Download references

Acknowledgements

This paper contains a full proof of results claimed in [11]. This work is partially supported by Russian Foundation for Fundamental Research (Grant 18-07-00566).

Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, Russia

    Roman Kolpakov

  2. Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Vavilov st. 40, Moscow, Russia

    Roman Kolpakov & Mikhail Posypkin

  3. National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, Moscow, 101000, Russia

    Mikhail Posypkin

Authors
  1. Roman Kolpakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mikhail Posypkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roman Kolpakov.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kolpakov, R., Posypkin, M. The scalability analysis of a parallel tree search algorithm. Optim Lett 14, 2211–2226 (2020). https://doi.org/10.1007/s11590-020-01547-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-020-01547-6

Keywords

Search

Navigation