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A molecular solution for minimum vertex cover problem in tile assembly model

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Abstract

Self-assembly is a generalization of the crystal growth, which has been proposed as a mechanism for the bottom-up fabrication of autonomous DNA computation. In the same context, tile assembly model is a highly distributed parallel model of natural self-assembly. In this paper, we propose a tile assembly system to tackle a well-known NP-complete problem known as Minimum Vertex Cover problem. The proposed algorithm requires Θ(n×m) types of tiles, and each parallel assembly executes in a linear time, where n is the number of vertices and m is the number of edges. Furthermore, the experimental results proved the simplicity and the efficiency of the proposed algorithm to solve the Minimum Vertex Cover, and reduce the overall complexity to find the solution.

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Acknowledgements

This work was partially funded by the Key Program of National Natural Science Foundation of China (Grant No. 61133005), and the National Natural Science Foundation of China (Grant Nos. 61070057, 61103047). Key Projects in the National Science & Technology Pillar Program (2012BAH09B02). The Ph.D. Programs Foundation of Ministry of Education of China (20100161110019). The project supported by the National Science Foundation for Distinguished Young Scholars of Hunan (12JJ1011). The Hunan Provincial Science and technology plan project (Grant No. 2012WK3053). The project supported by Scientific Research Fund of Hunan Provincial Education Department (Grant No.12A062). The Project of National Natural Science Foundation of China (Grant 61173013 and 61202109), The Project of the Office of Education in Zhejiang Province (Grant Y201226110).

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Authors and Affiliations

  1. College of Information Science and Technology, Hunan University, Changsha, 410082, China

    Fan Wu, Kenli Li, Ahmed Sallam & Xu Zhou

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  1. Fan Wu
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  2. Kenli Li
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  3. Ahmed Sallam
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  4. Xu Zhou
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Corresponding author

Correspondence to Kenli Li.

Appendix

Appendix

Several snapshots (Figs. 14, 15, 16 and 17) for applying the proposed algorithm using Xgrow simulator.

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A seed configuration with vertex set {1,3,4}

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Final configuration with vertex set {2,4,5}

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Final configuration with vertex set {1,3,4}

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Fig. 17
figure 18

Final configuration with vertex set {1,2,3,4}

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Wu, F., Li, K., Sallam, A. et al. A molecular solution for minimum vertex cover problem in tile assembly model. J Supercomput 66, 148–169 (2013). https://doi.org/10.1007/s11227-013-0892-0

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