Skip to main content
SpringerLink
Log in

Randomized Minimum Spanning Tree

1995; Karger, Klein, Tarjan

  • Reference work entry
Encyclopedia of Algorithms

  • 353 Accesses

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 399.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Recommended Reading

  1. Borůvka, O.: O jistém problému minimálním. Práce Moravské Přírodovědecké Společnosti 3, 37–58 (1926) (In Czech)

    Google Scholar 

  2. Buchsbaum, A., Kaplan, H., Rogers, A., Westbrook, J.R.: Linear-time pointer‐machine algorithms for least common ancestors, MST verification and dominators. In: Proc. ACM Symp. on Theory of Computing (STOC), 1998, pp. 279–288

    Google Scholar 

  3. Chan, T.M.: Backward analysis of the Karger–Klein–Tarjan algorithm for minimum spanning trees. Inf. Process. Lett. 67, 303–304 (1998)

    Article  Google Scholar 

  4. Chazelle, B.: A minimum spanning tree algorithm with inverse‐Ackermann type complexity. J. ACM 47(6), 1028–1047 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  6. Dixon, B., Rauch, M., Tarjan, R.E.: Verification and sensitivity analysis of minimum spanning trees in linear time. SIAM J. Comput. 21(6), 1184–1192 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gabow, H.N., Galil, Z., Spencer, T.H., Tarjan, R.E.: Efficient algorithms for finding minimum spanning trees in undirected and directed graphs. Comb. 6, 109–122 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  8. Graham, R.L., Hell, P.: On the history of the minimum spanning tree problem. Ann. Hist. Comput. 7(1), 43–57 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  9. Karger, D.R., Klein, P.N., Tarjan, R.E.: A randomized linear-time algorithm for finding minimum spanning trees. J. ACM 42(2), 321–329 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Karp, R.M., Ramachandran, V.: Parallel algorithms for shared‐memory machines. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, pp. 869–941. Elsevier Science Publishers B.V., Amsterdam (1990)

    Google Scholar 

  11. Katriel, I., Sanders, P., Träff, J.L.: A practical minimum spanning tree algorithm using the cycle property. In: Proc. 11th Annual European Symposium on Algorithms. LNCS, vol. 2832, pp. 679–690. Springer, Berlin (2003)

    Google Scholar 

  12. King, V.: A simpler minimum spanning tree verification algorithm. Algorithmica 18(2), 263–270 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  13. Komlós, J.: Linear verification for spanning trees. Combinatorica 5(1), 57–65 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pettie, S., Ramachandran, V.: An optimal minimum spanning tree algorithm. J. ACM 49(1), 16–34 (2002)

    Article  MathSciNet  Google Scholar 

  15. Pettie, S., Ramachandran, V.: A randomized time-work optimal parallel algorithm for finding a minimum spanning forest. SIAM J. Comput. 31(6), 1879–1895 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  16. Pettie, S., Ramachandran, V.: Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms. In: Proc. ACM-SIAM Symp. on Discrete Algorithms (SODA), 2002, pp. 713–722

    Google Scholar 

  17. Pettie, S., Ramachandran, V.: New randomized minimum spanning tree algorithms using exponentially fewer random bits. ACM Trans. Algorithms. 4(1), article 5 (2008)

    Google Scholar 

Download references

Acknowledgments

This work was supported in part by NSF grant CFF-0514876.

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Texas at Austin, Austin, TX, USA

    Vijaya Ramachandran

Authors
  1. Vijaya Ramachandran
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Ramachandran, V. (2008). Randomized Minimum Spanning Tree. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_325

Download citation

Publish with us

Policies and ethics

Search

Navigation