A DNA procedure for solving the shortest path problem

Wang, Zhaocai; Xiao, Dongmei; Li, Wenxia

doi:10.1016/j.amc.2006.05.061

Cited by 17 publications

(8 citation statements)

References 10 publications

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“…Other relative works are described for example in the Refs. [4][5][6][7][8]. In normal conditions quantum theory is needed to represent the mathematical description of problem.…”

Section: Discussionmentioning

confidence: 99%

A New Algorithm for Set Splitting Problem Based DNA Molecules Computation

Wang¹,

Tang²,

Liu³

et al. 2014

jnl of comp & theo nano

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The set splitting problem is to find a subset in a given set, that the sum of the subset is half of the whole set. In this paper, we present a DNA algorithm for solving set splitting problem with DNA molecular operations. For a set with n elements, we reasonably design fixed length DNA strands representing elements of the set, take appropriate steps and get the solutions of the set splitting problem in proper length range using O n time complexity.

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“…Other relative works are described for example in the Refs. [4][5][6][7][8]. In normal conditions quantum theory is needed to represent the mathematical description of problem.…”

Section: Discussionmentioning

confidence: 99%

A New Algorithm for Set Splitting Problem Based DNA Molecules Computation

Wang¹,

Tang²,

Liu³

et al. 2014

jnl of comp & theo nano

Self Cite

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“…Given a tube, one can perform the following operations: 6 Merge, Copy, Detect, Separation, Selection, Cleavage, Annealing, Ligation, Denaturation, Discard, Append and Read. Since above twelve manipulations are implemented with a constant number of biological steps for DNA strands, 6 we assume that the complexity of each manipulation is O 1 steps. These operations will be used for figuring out solutions of the minimum vertex cover problem in this paper.…”

Section: The Adleman-lipton Modelmentioning

confidence: 99%

“…In recent years, A lot of DNA procedures and algorithms have occurred to solve various NP-complete problems. [3][4][5][6][7][8][9][10][11][12] However, most of the previous works are concentrated on path search problems, that the optimum results are continuous head-to-tail ligation edges or vertex sets. The previous researches have some insufficient factors.…”

Section: Introductionmentioning

confidence: 99%

Solving the Minimum Vertex Cover Problem with DNA Molecules in Adleman-Lipton Model

Wang¹,

Huang²,

Pei³

2014

Jnl of Comp & Theo Nano

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The minimum vertex cover (MVC) problem is a vitally important NP-complete problem in graph theory and applied mathematics. In this paper, we present a DNA algorithm for solving the MVC problem with DNA molecular operations. For an undirected graph with n vertex, We reasonably design fixed length DNA strands representing the vertex and edges, take appropriate steps and get the solutions in proper length range using O n 2 time.

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“…Given a test tube, we can take the following operations: Merge, Copy, Detect, Separation, Selection, Cleavage, Annealing, Denaturation, Ligation, Discard, Read and Append-tail. Since these manipulations are implemented with a constant number of biological steps with DNA strands, [3][4][5][6][7][8][9][10][11][12][13] we assume that the complexity of each manipulation is O 1 steps.…”

Section: The Adleman-lipton Modelmentioning

confidence: 99%