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

Mahammad Maharram Aliyev

doi:doi:10.11648/j.acm.20140305.21

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

Mahammad Maharram Aliyev

Published in Applied and Computational Mathematics (Volume 3, Issue 5)

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), 2024. 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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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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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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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},
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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.},
 year = {2014}
}

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TY  - JOUR
T1  - Exact, Polynomial, Determination Solution Method of the Subset Sum Problem
AU  - Mahammad Maharram Aliyev
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PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.21
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JF  - Applied and Computational Mathematics
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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
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ER  -

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Author Information

Mahammad Maharram Aliyev

National Academy of Sciences of Azerbaijan, Institute of Control Systems, Baku, Azerbaijan

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Exact, Polynomial, Determination Solution Method of the Subset Sum Problem
AU  - Mahammad Maharram Aliyev
Y1  - 2014/11/10
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.21
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
SN  - 2328-5613
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  -

Copy | Download