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Exact, Polynomial, Determination Solution Method of the Subset Sum Problem

Received: 13 October 2014     Accepted: 28 October 2014     Published: 10 November 2014
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Abstract

In this paper we give original geometrical interpretation to the domain of definition of integer and combinatorial problems. The solution of the problems concerning NP class has been carried out on the hyperarches. The existence criterion of the solution on the hyperarches has been defined. The method for establishing the sequence of approximation to the solution on the hyperarches was constructed. Calculation experiments were conducted, and the obtained polynomial algorithm, practically and theoretically solved exactly the (SSP) problem.

Published in Applied and Computational Mathematics (Volume 3, Issue 5)
DOI 10.11648/j.acm.20140305.21
Page(s) 262-267
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Knapsack Problem (KP), Subset Sum Problem (SSP), NP Class, Integer Programming, N-Dimensional Cube, Hyper Plane, Hyper Circle, Hyper Arch

References
[1] Hans Kellerer, Ulrich Pferschy, David Pisinger Knapsack Problems. Spinger-Verlag Berlin. Hidelberg, 2004, 525 p.
[2] Мину М. Математические программирование. Москва, Наука 1990, 485 c.
[3] Aliyev M.M. One approach to the solution of the knapsack problem//Reports NAS of Azerb., 2005, №3, p.32-39.
[4] Aliyev M.M. On Solution Method of the Knapsack Problem. Proceedings of the Sixth International Conference on Management Science and Engineering Management. Volume I, Springer-Verlag, London, 2013, p.257-267.
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  • APA Style

    Mahammad Maharram Aliyev. (2014). Exact, Polynomial, Determination Solution Method of the Subset Sum Problem. Applied and Computational Mathematics, 3(5), 262-267. https://doi.org/10.11648/j.acm.20140305.21

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    ACS Style

    Mahammad Maharram Aliyev. Exact, Polynomial, Determination Solution Method of the Subset Sum Problem. Appl. Comput. Math. 2014, 3(5), 262-267. doi: 10.11648/j.acm.20140305.21

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    AMA Style

    Mahammad Maharram Aliyev. Exact, Polynomial, Determination Solution Method of the Subset Sum Problem. Appl Comput Math. 2014;3(5):262-267. doi: 10.11648/j.acm.20140305.21

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  • @article{10.11648/j.acm.20140305.21,
      author = {Mahammad Maharram Aliyev},
      title = {Exact, Polynomial, Determination Solution Method of the Subset Sum Problem},
      journal = {Applied and Computational Mathematics},
      volume = {3},
      number = {5},
      pages = {262-267},
      doi = {10.11648/j.acm.20140305.21},
      url = {https://doi.org/10.11648/j.acm.20140305.21},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.21},
      abstract = {In this paper we give original geometrical interpretation to the domain of definition of integer and combinatorial problems. The solution of the problems concerning NP class has been carried out on the hyperarches. The existence criterion of the solution on the hyperarches has been defined. The method for establishing the sequence of approximation to the solution on the hyperarches was constructed. Calculation experiments were conducted, and the obtained polynomial algorithm, practically and theoretically solved exactly the (SSP) problem.},
     year = {2014}
    }
    

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    T1  - Exact, Polynomial, Determination Solution Method of the Subset Sum Problem
    AU  - Mahammad Maharram Aliyev
    Y1  - 2014/11/10
    PY  - 2014
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    DO  - 10.11648/j.acm.20140305.21
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
    SP  - 262
    EP  - 267
    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.acm.20140305.21
    AB  - In this paper we give original geometrical interpretation to the domain of definition of integer and combinatorial problems. The solution of the problems concerning NP class has been carried out on the hyperarches. The existence criterion of the solution on the hyperarches has been defined. The method for establishing the sequence of approximation to the solution on the hyperarches was constructed. Calculation experiments were conducted, and the obtained polynomial algorithm, practically and theoretically solved exactly the (SSP) problem.
    VL  - 3
    IS  - 5
    ER  - 

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Author Information
  • National Academy of Sciences of Azerbaijan, Institute of Control Systems, Baku, Azerbaijan

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