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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     author = {D. M. Murin},
     title = {About some features of the transformed problems images},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {96--102},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2012_3_a10/}
}
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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/