Skip to main content
SpringerLink
Log in

Asynchronous parallel branch and bound and anomalies

  • Conference paper
  • First Online:
Parallel Algorithms for Irregularly Structured Problems (IRREGULAR 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 980))

Abstract

The parallel execution of branch and bound algorithms can result in seemingly unreasonable speedups or slowdowns. Almost never the speedup is equal to the increase in computing power. For synchronous parallel branch and bound, these effects have been studied extensively. For asynchronous parallelizations, only little is known.

In this paper, we derive sufficient conditions to guarantee that an asynchronous parallel branch and bound algorithm (with elimination by lower bound tests and dominance) will be at least as fast as its sequential counterpart. The technique used for obtaining the results seems to be more generally applicable.

The essential observations are that, under certain conditions, the parallel algorithm will always work on at least one node, that is branched from by the sequential algorithm, and that the parallel algorithm, after elimination of all such nodes, is able to conclude that the optimal solution has been found.

Finally, some of the theoretical results are brought into connection with a few practical experiments.

This work was partially supported by the Human Capital and Mobility project SCOOP — Solving Combinatorial Optimization Problems in Parallel — of the European Union.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F.W. Burton, M.M. Huntbach, G.P. McKeown, V.J. Rayward-Smith (1983). Parallelism in Branch-and-Bound Algorithms, Report CSA/3/1983, University of East Anglia, Norwich.

    Google Scholar 

  2. R. Corrêa, A. Ferreira (1995a). A distributed implementation of asynchronous parallel branch-and-bound. A. Ferreira & J. Rolim (eds.). Solving Irregular Problems in Parallel: State of the Art, Kluwer, Boston, to appear.

    Google Scholar 

  3. R. Corrêa, A. Ferreira (1995b). Modeling parallel branch-and-bound for asynchronous implementations. 1994 DIMACS Workshop on Parallel Processing of Discrete Optimization problems, DIMACS, Piscataway, to appear.

    Google Scholar 

  4. B.L. Fox, J.K. Lenstra, A.H.G. Rinnnooy Kan, L.E. Schrage (1978). Branching from the largest upper bound: folklore and facts. European J. Oper. Res. 2, 191–194.

    Article  Google Scholar 

  5. T. Ibaraki (1976). Theoretical comparisons of search strategies in branch-and-bound algorithms. Int. J. Comput. Inform. Sci. 5, 315–344.

    Article  Google Scholar 

  6. T. Ibaraki (1977). The power of dominance relations in branch-and-bound algorithms. J. Assoc. Comput. Mach. 24, 264–279.

    Google Scholar 

  7. T.-H. Lai, S. Sahni (1984). Anomalies in parallel branch-and-bound algorithms. Comm. ACM 27, 594–602.

    MathSciNet  Google Scholar 

  8. T.-H. Lai, A. Sprague (1985). Performance of parallel branch-and-bound algorithms. IEEE Trans. Comput. C-34, 962–964.

    Google Scholar 

  9. T.-H. Lai, A. Sprague (1986). A note on anomalies in parallel branch-and-bound algorithms with one-to-one bounding functions. Inform. Process. Lett. 23, 119–122.

    MathSciNet  Google Scholar 

  10. G.-J. Li, B.W. Wah (1984). Computational Efficiency of Parallel Approximate Branch-and-Bound Algorithms, Report TR-EE 84-6, Purdue University, West Lafayette.

    Google Scholar 

  11. G.-J. Li, B.W. Wah (1986). Coping with anomalies in parallel branch-and-bound algorithms. IEEE Trans. Comput. C-35, 568–573.

    MathSciNet  Google Scholar 

  12. G.P. McKeown, V.J. Rayward-Smith, S.A. Rush (1992). Parallel branch-and-bound. L. Kronsjoe, D. Shumsheruddin (eds.) Advances in Parallel Algorithms, Advanced Topics in Computer Science 14, Blackwell, Oxford, 111–150.

    Google Scholar 

  13. L.G. Mitten (1970). Branch-and-bound methods: general formulation and properties. Oper. Res. 18, 24–34.

    Google Scholar 

  14. H.W.J.M. Trienekens (1990). Parallel Branch and Bound Algorithms, Ph.D. thesis, Erasmus University, Rotterdam.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Erasmus University, P.O. Box 1738, 3000, DR Rotterdam, The Netherlands

    A. de Bruin, G. A. P. Kindervater & H. W. J. M. Trienekens

Authors
  1. A. de Bruin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. A. P. Kindervater
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. W. J. M. Trienekens
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Afonso Ferreira José Rolim

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

de Bruin, A., Kindervater, G.A.P., Trienekens, H.W.J.M. (1995). Asynchronous parallel branch and bound and anomalies. In: Ferreira, A., Rolim, J. (eds) Parallel Algorithms for Irregularly Structured Problems. IRREGULAR 1995. Lecture Notes in Computer Science, vol 980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60321-2_29

Download citation

  • DOI: https://doi.org/10.1007/3-540-60321-2_29

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60321-4

  • Online ISBN: 978-3-540-44915-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation