A DNA-based graph encoding scheme with its applications to graph isomorphism problems

• Published in: Applied mathematics and computation Vol. 203; no. 2; pp. 502 - 512
• Main Authors: Hsieh, Sun-Yuan, Huang, Chao-Wen, Chou, Hsin-Hung
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.09.2008; Elsevier
• Subjects: Biological operations; DNA-based algorithms; DNA-based computing; Exact sciences and technology; Mathematical analysis; Mathematics; Molecular computing; NP-complete; Numerical analysis; Numerical analysis. Scientific computation; Sciences and techniques of general use; The maximum common subgraph problem; The subgraph isomorphism problem; Molecular computing; The subgraph isomorphism problem; NP-complete; DNA-based algorithms; The maximum common subgraph problem; DNA-based computing; Biological operations; Polynomial; Combinatorial problem; Hamiltonian path; Optimization method; Combinatorial optimization; Algorithm; Implementation; Numerical analysis; Applied mathematics; DNA; Isomorphism; Problem solving; Subgraph; NP complete problem
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2008.04.041

Feynman first proposed DNA-based computation in 1961, but his idea was not implemented by experiment for a few decades. By properly manipulating DNA strands as the input instance of the Hamiltonian path problem, Adleman succeeded in solving the problem in a test tube. Since the experimental demonstration of its feasibility, DNA-based computing has been applied to a number of decision or combinatorial optimization problems. In this paper, we propose a DNA-based graph encoding scheme which can be used to solve some intractable graph problems, such as the subgraph isomorphism problem and its generalized problem – the maximum common subgraph problem, which are known to be NP-complete problems, in the Adleman–Lipton model using polynomial number of basic biological operations.