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Bloomfilter-Based Practical Kernelization Algorithms for Minimum Satisfiability

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Neural Information Processing (ICONIP 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1963))

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Abstract

Minimum Satisfiability problem (briefly, given a CNF formula, find an assignment satisfying the minimum number of clauses) has raised much attention recently. In the theoretical point of view, Minimum Satisfiability problem is fixed-parameterized, by transforming into Vertex Cover. However, such kind of transformation would be time-consuming, which takes \(O(m^2\cdot n)\) times to transform into Vertex Cover. We first present a \(O(m^2)\) filtering algorithm to transform MinSAT into Vertex cover with low false positive rate, by utilizing Bloom Filter structure. And then, instead of transformation to Vertex Cover, we present a practical kernelization rule directly on the original formula which takes time of \(O(L\cdot d(F))\), with a kernel size of \(k^2+k\).

This paper was supported by Supported by the National Natural Science Foundation of China under Grants (62002032, 62302060, 62372066) and Natural Science Foundation of Hunan Province of China under grant 2022JJ30620.

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Notes

  1. 1.

    Use the notation \(O^*(c^k)\) to denote the bound \(c^k n^{O(1)}\), where c is a positive number and n is the instance size.

  2. 2.

    https://maxsat-evaluations.github.io/.

References

  1. Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)

    Google Scholar 

  2. Chen, J., Kanj, I.: Improved exact algorithms for Max-SAT. Discret. Appl. Math. 142(1–3), 17–27 (2004)

    Article  MathSciNet  Google Scholar 

  3. Mahajan, M., Raman, V.: Parameterizing above guaranteed values: MaxSat and MaxCut. J. Algorithms 31(2), 335–354 (1999)

    Article  MathSciNet  Google Scholar 

  4. Chen, J., Xu, C., Wang, J.: Dealing with 4-variables by resolution: an improved MaxSAT algorithm. Theoret. Comput. Sci. 670, 33–44 (2017)

    Article  MathSciNet  Google Scholar 

  5. Kohli, R., Krishnamurti, R., Mirchandani, P.: The minimum satisfiability problem. SIAM J. Discret. Math. 7(2), 275–283 (1994)

    Article  MathSciNet  Google Scholar 

  6. Marathe, M.V., Ravi, S.S.: On approximation algorithms for the minimum satisfiability problem. Inf. Process. Lett. 58(1), 23–29 (1996)

    Article  MathSciNet  Google Scholar 

  7. Arif, U., Benkoczi, R., Gaur, D.R., et al.: A primal-dual approximation algorithm for Minsat. Discret. Appl. Math. 319, 372–381 (2022)

    Article  MathSciNet  Google Scholar 

  8. Markakis, E., Papasotiropoulos, G.: Computational aspects of conditional minisum approval voting in elections with interdependent issues. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pp. 304–310 (2020)

    Google Scholar 

  9. Ansotegui, C., Li, C.M., Manyá, F., et al.: A SAT-based approach to MinSAT. In: CCIA, pp. 185–189 (2012)

    Google Scholar 

  10. Li, C.M., Xiao, F., Manyá, F.: A resolution calculus for MinSAT. Logic J. IGPL 29(1), 28–44 (2021)

    Article  MathSciNet  Google Scholar 

  11. Heras, F., Morgado, A., Planes, J., et al.: Iterative SAT solving for minimum satisfiability. In: 2012 IEEE 24th International Conference on Tools with Artificial Intelligence, Athens Greece, pp. 922–927. IEEE(2012)

    Google Scholar 

  12. Li, C.M., Manyà, F., Quan, Z., Zhu, Z.: Exact MinSAT solving. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 363–368. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14186-7_33

    Chapter  Google Scholar 

  13. Li, C.M., Zhu, Z., Manya, F., et al.: Minimum satisfiability and its applications. In: Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, pp. 605–610. AAAI Press (2011)

    Google Scholar 

  14. Bliznets, I., Sagunov, D., Simonov, K.: Fine-grained complexity of partial minimum satisfiability. In: Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, pp. 1774–1780 (2022)

    Google Scholar 

  15. Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201–215 (1960)

    Article  MathSciNet  Google Scholar 

  16. Chen, J., Kanj, I., Jia, W.: Vertex cover: further observations and further improvements. J. Algorithms 41(2), 280–301 (2001)

    Article  MathSciNet  Google Scholar 

  17. Knuth, D.E., Morris, J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM J. Comput. 6(2), 323–350 (1997)

    Article  MathSciNet  Google Scholar 

  18. Wang, Z., Liu, K., Xu, C.: A bloom filter-based algorithm for fast detection of common variables. In: Proceedings of the 1st International Conference on the Frontiers of Robotics and Software Engineering (FRSE) (2023, accepted)

    Google Scholar 

  19. Bloom, B.H.: Space/time tradeoffs in hash coding with allowable errors. Commun. ACM 13(7), 422–426 (1970)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, 410003, Hunan, People’s Republic of China

    Chao Xu, Liting Dai & Kang Liu

Authors
  1. Chao Xu
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  2. Liting Dai
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  3. Kang Liu
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Corresponding author

Correspondence to Chao Xu .

Editor information

Editors and Affiliations

  1. School of Automation, Central South University, Changsha, China

    Biao Luo

  2. Institute of Automation, Chinese Academy of Sciences, Beijing, China

    Long Cheng

  3. Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China

    Zheng-Guang Wu

  4. School of Automation, Guangdong University of Technology, Guangzhou, China

    Hongyi Li

  5. School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW, Australia

    Chaojie Li

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Xu, C., Dai, L., Liu, K. (2024). Bloomfilter-Based Practical Kernelization Algorithms for Minimum Satisfiability. In: Luo, B., Cheng, L., Wu, ZG., Li, H., Li, C. (eds) Neural Information Processing. ICONIP 2023. Communications in Computer and Information Science, vol 1963. Springer, Singapore. https://doi.org/10.1007/978-981-99-8138-0_4

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  • DOI: https://doi.org/10.1007/978-981-99-8138-0_4

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