Geodesic
About some features of the transformed problems images
Prikladnaâ diskretnaâ matematika, no. 3 (2012), pp. 96-102.

Voir la notice de l'article provenant de la source Math-Net.Ru

One of the way to prove the NP-completeness of a problem is to transform in it polynomially a problem the NP-completeness of which we can prove. Herewith we pay less attention to the research of the received image features. In 1985 Lagarias and Odlyzko offered a method for solving knapsack NP-complete problem that gives a true decision for “near all” knapsacks with the density less than $0.6463\dots$ In this paper, we consider the following question: in which knapsack problems area (with regard to the knapsacks density) we can place, while proving the NP-completeness, the images of the problems such as $3$-SAT, Colouring, Exact cover.
Keywords: NP-completeness, Lagarias–Odlyzko method, knapsack problem. 
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D. M. Murin. About some features of the transformed problems images. Prikladnaâ diskretnaâ matematika, no. 3 (2012), pp. 96-102. http://geodesic.mathdoc.fr/item/PDM_2012_3_a10/

[1] Uspenskii V. A., Semenov A. L., Teoriya algoritmov: osnovnye otkrytiya i prilozheniya, Nauka, M., 1987, 288 pp. | MR

[2] Odlyzko A. M., Lagarias J. C., “Solving Low-Density Subset Sum Problems”, J. Association Computing Machinery, 32:1 (1985), 229–246 | DOI | MR | Zbl

[3] Vasilenko O. N., Teoretiko-chislovye algoritmy v kriptografii, MTsNMO, M., 2006, 336 pp.

[4] Coster M. J., Joux A., LaMacchia B. A., et al., “Improved low-density subset sum algorithms”, Computational Complexity, 2:2 (1992), 111–128 | DOI | MR | Zbl

[5] Karp R. M., “Reducibility among combinatorial problems”, Complexity of Computer Computations, Proc. of a Symp. on the Complexity of Computer Computations, the IBM Research Symposia Series, Plenum Press, NY, 1972, 85–103 | DOI | MR

[6] Kopson E. T., Asimptoticheskie razlozheniya, Mir, M., 1966, 159 pp.

[7] Akho A., Khopkroft Dzh., Ulman Dzh., Postroenie i analiz vychislitelnykh algoritmov, Mir, M., 1979, 536 pp. | MR