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Towards the Succinct Representation of m Out of n

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Internet and Distributed Computing Systems (IDCS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11226))

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Abstract

Combinations of n objects taken m at the time are ubiquitous in a wide range of combinatorial problems. In this paper, we introduce a novel approach to generate combinations from given integer numbers by using a gradient-based algorithm through plural number of CPU and GPU processors. The time complexity is bounded by \(O(m^2)\) when using a single processor, and bounded by \(O(m \log m)\) when using at most \(O(m/\log m)\) processors. Relevant computational experiments confirmed the practical efficiency within computationally allowable limits. Our approach offers the building blocks to represent combinations with succinct encoding and complexity being independent of n, which is meritorious when n is very large, or when n is time-varying.

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Notes

  1. 1.

    unless otherwise stated, \(\log ()\) refers to \(\log _2()\).

  2. 2.

    personal communication with Ref. [33].

  3. 3.

    assuming algebraic operations with numbers in O(1).

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Acknowledgement

We acknowledge the support from Kakenhi No. 15K18095 to fund this work.

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Authors and Affiliations

  1. Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Victor Parque & Tomoyuki Miyashita

  2. Egypt - Japan University of Science and Technology, Borg El Arab, Alexandria, 21934, Egypt

    Victor Parque

Authors
  1. Victor Parque
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  2. Tomoyuki Miyashita
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Corresponding author

Correspondence to Victor Parque .

Editor information

Editors and Affiliations

  1. Swinburne University of Technology, Hawthorn, VIC, Australia

    Yang Xiang

  2. National Institute of Informatics, Tokyo, Japan

    Jingtao Sun

  3. University of Calabria, Rende (CS), Italy

    Giancarlo Fortino

  4. ICAR-CNR, Rende (CS), Italy

    Antonio Guerrieri

  5. Chung-Ang University, Seoul, Korea (Republic of)

    Jason J. Jung

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Parque, V., Miyashita, T. (2018). Towards the Succinct Representation of m Out of n. In: Xiang, Y., Sun, J., Fortino, G., Guerrieri, A., Jung, J. (eds) Internet and Distributed Computing Systems. IDCS 2018. Lecture Notes in Computer Science(), vol 11226. Springer, Cham. https://doi.org/10.1007/978-3-030-02738-4_2

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  • DOI: https://doi.org/10.1007/978-3-030-02738-4_2

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