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Is optimal solution of every NP-complete or NP-hard problem determined from its characteristic for DNA-based computing
Ist Teil von
BioSystems, 2005-04, Vol.80 (1), p.71-82
Ort / Verlag
Ireland: Elsevier Ireland Ltd
Erscheinungsjahr
2005
Link zum Volltext
Quelle
MEDLINE
Beschreibungen/Notizen
Cook's Theorem [Cormen, T.H., Leiserson, C.E., Rivest, R.L., 2001. Introduction to Algorithms, second ed., The MIT Press; Garey, M.R., Johnson, D.S., 1979. Computer and Intractability, Freeman, San Fransico, CA] is that if one algorithm for an NP-complete or an NP-hard problem will be developed, then other problems will be solved by means of reduction to that problem. Cook's Theorem has been demonstrated to be correct in a general
digital electronic computer. In this paper, we first propose a DNA algorithm for solving the
vertex-cover problem. Then, we demonstrate that if the size of a reduced NP-complete or NP-hard problem is equal to or less than that of the vertex-cover problem, then the proposed algorithm can be directly used for solving the reduced NP-complete or NP-hard problem and Cook's Theorem is correct on DNA-based computing. Otherwise, a new DNA algorithm for optimal solution of a reduced NP-complete problem or a reduced NP-hard problem should be developed from the characteristic of NP-complete problems or NP-hard problems.