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A Fast Construction Algorithm for the Incidence Matrices of a Class of Symmetric Balanced Incomplete Block Designs

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Computational Science and Its Applications – ICCSA 2004 (ICCSA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3046))

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Abstract

The theory of symmetric balanced incomplete block designs (BIBDs) has been applied in many research areas such as colored graphs, visual cryptography, distributed systems, communication networks, etc. In this paper, an explicit formula for a class of symmetric BIBDs is presented. Based on this formula, an efficient algorithm for constructing the incidence matrix of the design is developed. The incidence matrix contains all essential information of the design. The computational costs of the algorithm are O(v) which are superior to those of O(v 2) or \(O(v\sqrt{v})\) by the conventional methods, where v is the number of objects or blocks.

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Author information

Authors and Affiliations

  1. Department of Mathematics & College of Pharmacy, Chosun University, Gwangju, 501-759, Korea

    Ju-Hyun Lee

  2. Department of Mathematics, Chosun University, Gwangju, 501-759, Korea

    Sungkwon Kang

  3. College of Pharmacy, Chosun University, Gwangju, 501-759, Korea

    Hoo-Kyun Choi

Authors
  1. Ju-Hyun Lee
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  2. Sungkwon Kang
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  3. Hoo-Kyun Choi
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Editor information

Editors and Affiliations

  1. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  5. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  6. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

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© 2004 Springer-Verlag Berlin Heidelberg

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Lee, JH., Kang, S., Choi, HK. (2004). A Fast Construction Algorithm for the Incidence Matrices of a Class of Symmetric Balanced Incomplete Block Designs. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24768-5_2

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  • DOI: https://doi.org/10.1007/978-3-540-24768-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22060-2

  • Online ISBN: 978-3-540-24768-5

  • eBook Packages: Springer Book Archive

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