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Molecular solutions for minimum and exact cover problems in the tile assembly model

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Abstract

The tile assembly model is a novel biological computing model where information is encoded in DNA tiles. It is an efficient way to solve NP-complete problems due to its scalability and parallelism. In this paper, we apply the tile assembly model to solve the minimum and exact set cover problems, which are well-known NP-complete problems. To solve the minimum set cover problem, we design a MinSetCover system composed of three parts, i.e., the seed configuration subsystem, the nondeterministic choice subsystem, and the detection subsystem. Moreover, we improve the MinSetCover system and propose a MinExactSetCover system for solving the problem of exact cover by 3-sets. Finally we analyze the computation complexity and perform a simulation experiment to verify the effectiveness and correctness of the proposed systems.

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Acknowledgments

This research is supported by the key Project of National Natural Science Foundation of China under grant 61133005, the Project of National Natural Science Foundation of China under grant 61173013 and 61202109, the Project of the Office of Education in Zhejiang Province under grant Y201226110.

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Authors and Affiliations

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

    Xu Zhou, YanTao Zhou, KenLi Li, Ahmed Sallam & Keqin Li

  2. College of Mathematics and Information Engineering, Jiaxing University, Jiaxing , 314001, China

    Keqin Li

  3. Department of Computer Science, State University of New York, New Paltz, NY , 12561, USA

    Xu Zhou

Authors
  1. Xu Zhou
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  2. YanTao Zhou
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  3. KenLi Li
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  4. Ahmed Sallam
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Corresponding author

Correspondence to Xu Zhou.

Appendix

Appendix

The simulation results by running the Xgrow simulator for solving our problem above (Figs. 20, 21).

Fig. 20
figure 20

The results of simulating the MinSetCover system by Xgrow

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Fig. 21
figure 21

The results of simulating the MinExtractSetCover system by Xgrow

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Zhou, X., Zhou, Y., Li, K. et al. Molecular solutions for minimum and exact cover problems in the tile assembly model. J Supercomput 69, 976–1005 (2014). https://doi.org/10.1007/s11227-014-1222-x

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  • DOI: https://doi.org/10.1007/s11227-014-1222-x

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