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Three Sorting Algorithms Using Priority Queues

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Algorithms and Computation (ISAAC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2906))

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Abstract

We establish a lower bound of B(n) = n⌈logn ⌉ − 2⌈logn⌉ + 1 on the number of comparisons performed by any algorithm that uses priority queues to sort n elements. Three sorting algorithms using priority queues are introduced. The first algorithm performs the same comparisons as the classical Mergesort algorithm, but in a different order. The second algorithm performs at most 2nlogn + O(n) comparisons, with the advantage of being adaptive; meaning that it runs faster when the input sequence has some presortedness. In particular, we show that this algorithm sorts an already sorted sequence in linear time; a fact that is not obvious since there is no special checks to guarantee this behavior. The third algorithm is almost implicit; it can be implemented using the input array and less than n extra bits. The number of comparisons performed by this algorithm is at most B(n)+2.5n. The three algorithms have the advantage of producing every element of the sorted output, after the first, in O(log n), and can be implemented to be practically efficient.

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Author information

Authors and Affiliations

  1. Computer Science Department, Alexandria University, Alexandria, Egypt

    Amr Elmasry

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  1. Amr Elmasry
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Editor information

Editors and Affiliations

  1. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Toshihide Ibaraki

  2. Department of Architecture and Architectural Engineering, Kyoto University, 615-8540, Nishikyo-ku, Kyoto, Japan

    Naoki Katoh

  3. Department of Computer Science and Communication Engineering, Kyushu University, 812-8581, Fukuoka, Japan

    Hirotaka Ono

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Elmasry, A. (2003). Three Sorting Algorithms Using Priority Queues. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_23

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  • DOI: https://doi.org/10.1007/978-3-540-24587-2_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20695-8

  • Online ISBN: 978-3-540-24587-2

  • eBook Packages: Springer Book Archive

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