Skip to main content
SpringerLink
Log in

A Distributed Parallel Algorithm for the Minimum Spanning Tree Problem

  • Conference paper
  • First Online:
Parallel Computational Technologies (PCT 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 753))

Included in the following conference series:

Abstract

In this paper, we present and evaluate a parallel algorithm for solving the minimum spanning tree (MST) problem on supercomputers with distributed memory. The algorithm relies on the relaxation of the message processing order requirement for one specific message type compared to the original GHS (Gallager, Humblet, Spira) algorithm. Our algorithm adopts hashing and message compression optimization techniques as well. To the best of our knowledge, this is the first parallel implementation of the GHS algorithm that linearly scales to more than 32 nodes (256 cores) of an InfiniBand cluster.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Minimum spanning trees. Introduction to Algorithms, 2nd edn, pp. 561–579. MIT Press and McGraw-Hill, Cambridge (2001). Chap. 23

    Google Scholar 

  2. Rubanov, L.I., Seliverstov, A.V., Zverkov, O.A.: Ultraconservative elements in the simplest of subtype Alveolata. Modern Inf. Technol. IT Educ. 2, 581–585 (2015)

    Google Scholar 

  3. Eisner, J.: State-of-the-art algorithms for minimum spanning trees. A Tutorial Discussion, University of Pennsylvania (1997)

    Google Scholar 

  4. Prim, R.C.: Shortest connection networks and some generalizations. Bell Syst. Tech. J. 36, 1389–1401 (1957)

    Article  Google Scholar 

  5. Kruskal, J.B.: On the shortest spanning subtree of a graph and the traveling salesman problem. AMS 7, 48–50 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  6. Boruvka, O.: O jistem problemu minimalnim (about a certain minimal problem). Prace Mor. Prirodoved. Spol. v Brne, III 3, 37–58 (1926)

    Google Scholar 

  7. Kolganov, A.S.: Parallel implementation of minimum spanning tree algorithm on CPU and GPU. Parallel computational technologies (2016)

    Google Scholar 

  8. Mariano, A., Lee, D., Gerstlauer, A., Chiou, D.: Hardware and software implementations of Prim’s algorithm for efficient minimum spanning tree computation. In: Schirner, G., Götz, M., Rettberg, A., Zanella, M.C., Rammig, F.J. (eds.) IESS 2013. IAICT, vol. 403, pp. 151–158. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38853-8_14

    Chapter  Google Scholar 

  9. Wang, W., Huang, Y., Guo, S.: Design and implementation of GPU-based Prim’s algorithm. Int. J. Modern Educ. Comput. Sci. 3(4), 55–62 (2011)

    Article  Google Scholar 

  10. Katsigiannis, A., Anastopoulos, N., Nikas, K.: An approach to parallelize Kruskal’s algorithm using helper threads. In: IEEE 26th International Parallel and Distributed Processing Symposium Workshops and PhD Forum, pp. 1601–1610 (2012)

    Google Scholar 

  11. Gallager, R.G., Humblet, P.A., Spira, P.M.: A distributed algorithm for minimum-weight spanning trees. ACM Trans. Program. Lang. Syst. 5, 66–77 (1983)

    Article  MATH  Google Scholar 

  12. Awerbuch, B.: Optimal distributed algorithms for minimum weight spanning tree, Counting, Leader Election, and Related Problems. In: 19th ACM Symposium on Theory of Computing (STOC), New York, pp. 230–240 (1987)

    Google Scholar 

  13. Gregor, D., Lumsdaine, A.: The parallel BGL: a generic library for distributed graph computations. In: Parallel Object-Oriented Scientific Computing (2005)

    Google Scholar 

  14. Loncar, V., Skrbic, S.: Parallel implementation of minimum spanning tree algorithms using MPI. In: IEEE 13th International Symposium on Computational Intelligence and Informatics (CINTI), pp. 35–38 (2012)

    Google Scholar 

  15. Loncar, V., Skrbic, S., Balaz, A.: Parallelization of minimum spanning tree algorithms using distributed memory architectures (2014)

    Google Scholar 

  16. Sireta, A.: Comparison of parallel and distributed implementation of the MST algorithm (2016). http://delaat.net/rp/2015-2016/p41/report.pdf

  17. Ramaswamy, S.I., Patki, R.: Distributed minimum spanning trees (2015). http://stanford.edu/~rezab/classes/cme323/S15/projects/distributed_minimum_spanning_trees_report.pdf

  18. McCune, R.R., Weninger, T., Madey, G.: Thinking like a vertex: a survey of vertex-centric frameworks for distributed graph processing. ACM Comput. Surv. 48 (2015)

    Google Scholar 

  19. Knuth, D.: The Art of Computer Programming, 2nd edn., vol. 3, pp. 513–558. Addison-Wesley (1998)

    Google Scholar 

  20. Chakrabarti, D., Zhan, Y., Faloutsos, C.: R-MAT: a recursive model for graph mining. In: Proceedings of the Fourth SIAM International Conference on Data Mining (2004). http://repository.cmu.edu/cgi/viewcontent.cgi?article=1541&context=compsci

  21. Bader, D.A., Madduri, K.: Design and implementation of the HPCS graph analysis benchmark on symmetric multiprocessors. In: Bader, D.A., Parashar, M., Sridhar, V., Prasanna, V.K. (eds.) HiPC 2005. LNCS, vol. 3769, pp. 465–476. Springer, Heidelberg (2005). doi:10.1007/11602569_48

    Chapter  Google Scholar 

  22. Erdoos, P., Reyni, A.: On random graphs. I. Publicationes Math. 6, 290–297 (1959)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. JSC NICEVT, Moscow, Russia

    Artem Mazeev, Alexander Semenov & Alexey Simonov

Authors
  1. Artem Mazeev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Semenov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexey Simonov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Semenov .

Editor information

Editors and Affiliations

  1. South Ural State University, Chelyabinsk, Russia

    Leonid Sokolinsky

  2. South Ural State University, Chelyabinsk, Russia

    Mikhail Zymbler

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Mazeev, A., Semenov, A., Simonov, A. (2017). A Distributed Parallel Algorithm for the Minimum Spanning Tree Problem. In: Sokolinsky, L., Zymbler, M. (eds) Parallel Computational Technologies. PCT 2017. Communications in Computer and Information Science, vol 753. Springer, Cham. https://doi.org/10.1007/978-3-319-67035-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-67035-5_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67034-8

  • Online ISBN: 978-3-319-67035-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation