Exact, Polynomial, Determination Solution Method of the Subset Sum Problem
Applied and Computational Mathematics
Volume 3, Issue 5, October 2014, Pages: 262-267
Received: Oct. 13, 2014; Accepted: Oct. 28, 2014; Published: Nov. 10, 2014
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Author
Mahammad Maharram Aliyev, National Academy of Sciences of Azerbaijan, Institute of Control Systems, Baku, Azerbaijan
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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.
Keywords
Knapsack Problem (KP), Subset Sum Problem (SSP), NP Class, Integer Programming, N-Dimensional Cube, Hyper Plane, Hyper Circle, Hyper Arch
To cite this article
Mahammad Maharram Aliyev, Exact, Polynomial, Determination Solution Method of the Subset Sum Problem, Applied and Computational Mathematics. Vol. 3, No. 5, 2014, pp. 262-267. doi: 10.11648/j.acm.20140305.21
References
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Hans Kellerer, Ulrich Pferschy, David Pisinger Knapsack Problems. Spinger-Verlag Berlin. Hidelberg, 2004, 525 p.
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Мину М. Математические программирование. Москва, Наука 1990, 485 c.
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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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