Skip to main content

O(1) Time Algorithm on BSR for Constructing a Binary Search Tree with Best Frequencies

  • Conference paper
Parallel and Distributed Computing: Applications and Technologies (PDCAT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3320))

Abstract

Constructing a binary search tree of n nodes with best frequencies needs Ω(n log n) time on RAM, and Ω(log n) time on n-processor EREW, CREW, or CRCW PRAM. In this paper, we propose an O(1) time algorithm on n-processor BSR PRAM for the problem, which is the first constant time solution to the problem on any model of computation.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Devroye, L., Robson, J.M.: On the generation of random binary search tree. SIAM J. Comput. 24(6), 1141–1156 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Xiang, L., Ushijima, K.: On time bounds, the work-time scheduling principle, and optimality for BSR. IEEE Trans. on Parallel and Distributed Systems 12(9), 912–921 (2001)

    Article  Google Scholar 

  3. Akl, S.G.: Parallel Computation: Models and Methods, pp. 475–509. Prentice Hall, N.J (1997)

    Google Scholar 

  4. Lindon, L.F., Akl, S.G.: An Optimal Implementation of Broadcasting with Selective Reduction. IEEE Trans. on Parallel and Distributed Systems 4(3), 256–269 (1993)

    Article  Google Scholar 

  5. Xiang, L., Ushijima, K., Akl, S.G., Stojmenovic, I.: An Efficient Implementation for the BROADCAST Instruction of BSR+. IEEE Trans. on Parallel and Distributed Systems 10(8), 852–863 (1999)

    Article  Google Scholar 

  6. Stojmenovic, I.: Constant time BSR solutions to parenthesis matching, tree decoding, and tree reconstruction from its traversals. IEEE Trans. on Parallel and Distributed Systems 7(2), 218–224 (1996)

    Article  Google Scholar 

  7. Xiang, L., Ushijima, K.: Decoding and drawing an arbitrary tree from its pre-post sequence. In: Proc. PDCS 1998, Las Vegas, pp. 182–185 (1998)

    Google Scholar 

  8. Xiang, L., Ushijima, K.: Optimal Parallel Merging Algorithms on BSR. In: Proc. I-SPAN 2000, Dallas, pp. 12–17 (2000)

    Google Scholar 

  9. Xiang, L., Ushijima, K.: O(1) Time Algorithm on BSR for Computing Convex Hull. In: Proc. PDCS 2002, Cambridge, USA, pp. 143–146 (2002)

    Google Scholar 

  10. Xiang, L., Ushijima, K.: ANSV problem on BSRs. Information Processing Letters 65(3), 135–138 (1998)

    Article  MathSciNet  Google Scholar 

  11. Xiang, L., Ushijima, K.: Decoding and drawing on BSR for a binary tree from its i-p sequence. Parallel Processing Letters 9(1), 103–110 (1999)

    Article  MathSciNet  Google Scholar 

  12. Xiang, L., Ushijima, K.: Rearranging scattered information on BSR. Information Processing Letters 71(1), 43–47 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. Xiang, L., Ushijima, K.: A theorem on the relation between BSR k and BSR  + . Information Processing Letters 71(2), 71–73 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. Xiang, L., Ushijima, K., Zhao, J.: Time Optimal n-Size Matching Parentheses and Binary Tree Decoding Algorithms on a p-Processor BSR. Parallel Processing Letters 12(3-4), 365–374 (2002)

    Article  MathSciNet  Google Scholar 

  15. Xiang, L., Ushijima, K., Zhao, J., Zhang, T., Tang, C.: O(1) Time Algorithm on BSR for Constructing a Random Binary Search Tree. In: Liew, K.-M., Shen, H., See, S., Cai, W. (eds.) PDCAT 2004. LNCS, vol. 3320, pp. 218–225. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Xiang, L., Ushijiam, K., Cheng, K., Zhao, J., Lu, C. (2004). O(1) Time Algorithm on BSR for Constructing a Binary Search Tree with Best Frequencies. In: Liew, KM., Shen, H., See, S., Cai, W., Fan, P., Horiguchi, S. (eds) Parallel and Distributed Computing: Applications and Technologies. PDCAT 2004. Lecture Notes in Computer Science, vol 3320. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30501-9_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30501-9_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24013-6

  • Online ISBN: 978-3-540-30501-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics