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A Tight Bound on the Worst-Case Number of Comparisons for Floyd’s Heap Construction Algorithm

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Book cover Optimization Theory, Decision Making, and Operations Research Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 31))

Abstract

In this paper a tight bound on the worst-case number of comparisons for Floyd’s well-known heap construction algorithm is derived.1 It is shown that at most \(2n - 2\mu (n) - \sigma (n)\) comparisons are executed in the worst case, where μ(n) is the number of ones and σ(n) is the number of zeros after the last one in the binary representation of the number of keys n.

1This paper was also presented at Student Research Forum of SOFSEM’11 [Paparrizos, A tight bound on the worst-case number of comparisons for Floyd’s heap construction algorithm (2011)].

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References

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Author information

Authors and Affiliations

  1. Computer Science Department, Columbia University, New York, NY, USA

    Ioannis Paparrizos

Authors
  1. Ioannis Paparrizos
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Corresponding author

Correspondence to Ioannis Paparrizos .

Editor information

Editors and Affiliations

  1. , Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece

    Athanasios Migdalas

  2. , Economical and Social Sciences, University of Macedonia, Loggou-Tourpali, Naoussa, 59200, Greece

    Angelo Sifaleras

  3. , Department of Applied Informatics, University of Macedonia, Egnatia St. 156, Thessaloniki, 54006, Greece

    Christos K. Georgiadis

  4. , Department of Marketing and Operations M, University of Macedonia, Agiou Dimitriou 49, Edessa, 58200, Greece

    Jason Papathanasiou

  5. , Department of Applied Informatics, University of Macedonia, Egnatia Street 156, Thessaloniki, 54006, Greece

    Emmanuil Stiakakis

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Paparrizos, I. (2013). A Tight Bound on the Worst-Case Number of Comparisons for Floyd’s Heap Construction Algorithm. In: Migdalas, A., Sifaleras, A., Georgiadis, C., Papathanasiou, J., Stiakakis, E. (eds) Optimization Theory, Decision Making, and Operations Research Applications. Springer Proceedings in Mathematics & Statistics, vol 31. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5134-1_10

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