Solving the set cover problem and the problem of exact cover by 3-sets in the Adleman–Lipton model

• Published in: BioSystems Vol. 72; no. 3; pp. 263 - 275
• Main Authors: Chang, Weng-Long, Guo, Minyi
• Format: Journal Article
• Language: English
• Published: Ireland Elsevier Ireland Ltd 01.12.2003
• Subjects: Algorithms; Biological computing; DNA - chemistry; DNA-based computing; Models, Biological; Models, Genetic; Models, Molecular; Models, Theoretical; Molecular computing; Software; Statistics as Topic - methods; The NP-complete problem; The NP-complete problem; Biological computing; Molecular computing; DNA-based computing
• ISSN: 0303-2647; 1872-8324
• DOI: 10.1016/S0303-2647(03)00149-7

Adleman wrote the first paper in which it is shown that deoxyribonucleic acid (DNA) strands could be employed towards calculating solutions to an instance of the NP-complete Hamiltonian path problem (HPP). Lipton also demonstrated that Adleman’s techniques could be used to solve the NP-complete satisfiability (SAT) problem (the first NP-complete problem). In this paper, it is proved how the DNA operations presented by Adleman and Lipton can be used for developing DNA algorithms to resolving the set cover problem and the problem of exact cover by 3 -sets.