On the General Coloring Problem

A DNA computer model for solving vertex coloring problem

Chinese Science Bulletin ◽

10.1007/s11434-006-2145-6 ◽

2006 ◽

Vol 51 (20) ◽

pp. 2541-2549 ◽

Cited By ~ 15

Author(s):

Jin Xu ◽

Xiaoli Qiang ◽

Fang Gang ◽

Kang Zhou

Keyword(s):

Computer Model ◽

Vertex Coloring ◽

Coloring Problem ◽

Vertex Coloring Problem ◽

Dna Computer

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Adaptive Petri net based on irregular cellular learning automata with an application to vertex coloring problem

Applied Intelligence ◽

10.1007/s10489-016-0831-x ◽

2016 ◽

Vol 46 (2) ◽

pp. 272-284 ◽

Cited By ~ 16

Author(s):

S. Mehdi Vahidipour ◽

Mohammad Reza Meybodi ◽

Mehdi Esnaashari

Keyword(s):

Petri Net ◽

Learning Automata ◽

Vertex Coloring ◽

Coloring Problem ◽

Vertex Coloring Problem ◽

Cellular Learning Automata

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A parallel biological computing algorithm to solve the vertex coloring problem with polynomial time complexity

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-200025 ◽

2021 ◽

pp. 1-11

Author(s):

Zhaocai Wang ◽

Dangwei Wang ◽

Xiaoguang Bao ◽

Tunhua Wu

Keyword(s):

Time Complexity ◽

Optimization Problems ◽

Combinatorial Problem ◽

Vertex Coloring ◽

Intelligent Computing ◽

Coloring Problem ◽

Combinatorial Optimization Problems ◽

Computing Algorithm ◽

Vertex Coloring Problem ◽

Dna Algorithm

The vertex coloring problem is a well-known combinatorial problem that requires each vertex to be assigned a corresponding color so that the colors on adjacent vertices are different, and the total number of colors used is minimized. It is a famous NP-hard problem in graph theory. As of now, there is no effective algorithm to solve it. As a kind of intelligent computing algorithm, DNA computing has the advantages of high parallelism and high storage density, so it is widely used in solving classical combinatorial optimization problems. In this paper, we propose a new DNA algorithm that uses DNA molecular operations to solve the vertex coloring problem. For a simple n-vertex graph and k different kinds of color, we appropriately use DNA strands to indicate edges and vertices. Through basic biochemical reaction operations, the solution to the problem is obtained in the O (kn2) time complexity. Our proposed DNA algorithm is a new attempt and application for solving Nondeterministic Polynomial (NP) problem, and it provides clear evidence for the ability of DNA calculations to perform such difficult computational problems in the future.

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