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Heap Building Bounds

  • Zhentao Li
  • Bruce A. Reed
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3608)

Abstract

We consider the lower bound for building a heap in the worst case and the upper bound in the average case. We will prove that the supposedly fastest algorithm in the average case[2] does not attain its claimed bound and indeed is slower than that in [6]. We will then prove that the adversarial argument for the claimed best lower bound in the worst case[1] is also incorrect and the adversarial argument used yields a bound which is worse than that in [5] given by an information theory argument. Finally, we have proven a lower bound of 1.37n + o(n) for building a heap in the worst case.

Keywords

Fast Algorithm Average Case Left Child Binomial Tree Extra Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Carlsson, S., Chen, J.: The complexity of heaps. In: Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms, pp. 393–402. SIAM, Philadelphia (1992)Google Scholar
  2. 2.
    Carlsson, S., Chen, J.: Heap construction: Optimal in both worst and average cases? In: Algorithms and Computation, pp. 254–263. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  3. 3.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Sten, C.: Introduction to Algorithms, 2nd edn. The MIT Press, McGraw-Hill Book Company (2001)Google Scholar
  4. 4.
    Floyd, R.W.: Algorithm 245: Treesort. Commun. ACM 7(12), 701 (1964)CrossRefGoogle Scholar
  5. 5.
    Gonnet, G.H., Munro, I.: Heaps on heaps. SIAM Journal of Computing 15(4), 964–971 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    McDiarmid, C.J., Reed, B.A.: Building heaps fast. J. Algorithms 10(3), 352–365 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Williams, J.W.J.: Algorithm 232: Heapsort. Commun. of the ACM 7(6), 347–348 (1964)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Zhentao Li
    • 1
  • Bruce A. Reed
    • 1
  1. 1.School of Computer ScienceMcGill University 

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