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Solving the Bin-Packing Problem by Means of Tissue P System with 2-Division

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Unconventional Computation and Natural Computation (UCNC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10240))

Abstract

The ability of tissue P systems with 2-division for solving NP problems in polynomial time is well-known and many solutions can be found in the literature to several of such problems. Nonetheless, there are very few papers devoted to the Bin-packing problem. The reason may be the difficulties for dealing with different number of bins, capacity and number of objects by using exclusively division rules that produce two offsprings in each application. In this paper we present the design of a family of tissue P systems with 2 division which solves the Bin-packing problem in polynomial time by combining design techniques which can be useful for further research.

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Notes

  1. 1.

    Such solutions are technically correct, but, of course, the exponential generation of new working space has evident limits from a practical point of view. Any practical implementation of P systems solving NP-problems with physical support only could solve small instances of the problem.

  2. 2.

    The reader is supposed to be familiar with the basic concepts of membrane computing. See [29] for details.

  3. 3.

    \(T_i\) and \(F_i\) stand for True and False in the \(i-th\) position and, as usual, represents 1 and 0 in a binary representation.

  4. 4.

    As usual, we omit the parameters in the description for the sake of readability.

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Authors and Affiliations

  1. Karunya University, Coimbatore, Tamilnadu, India

    Hepzibah A. Christinal, Rose Rani John & D. Abraham Chandy

  2. Department of Computer Science and Artificial Intelligence, University of Seville, 41012, Seville, Spain

    Miguel A. Gutiérrez-Naranjo

Authors
  1. Hepzibah A. Christinal
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  2. Rose Rani John
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  3. D. Abraham Chandy
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  4. Miguel A. Gutiérrez-Naranjo
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Correspondence to Hepzibah A. Christinal .

Editor information

Editors and Affiliations

  1. University of Arkansas, Fayetteville, Arkansas, USA

    Matthew J. Patitz

  2. University of Sheffield, Sheffield, United Kingdom

    Mike Stannett

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Christinal, H.A., John, R.R., Chandy, D.A., Gutiérrez-Naranjo, M.A. (2017). Solving the Bin-Packing Problem by Means of Tissue P System with 2-Division. In: Patitz, M., Stannett, M. (eds) Unconventional Computation and Natural Computation. UCNC 2017. Lecture Notes in Computer Science(), vol 10240. Springer, Cham. https://doi.org/10.1007/978-3-319-58187-3_13

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  • DOI: https://doi.org/10.1007/978-3-319-58187-3_13

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