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International Workshop on Algorithms and Computation

WALCOM 2018: WALCOM: Algorithms and Computation pp 93–105Cite as

An Improvement of the Algorithm of Hertli for the Unique 3SAT Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10755))

Abstract

We propose a simple idea for improving the randomized algorithm of Hertli for the Unique 3SAT problem. Using recently developed techniques, we can derive from this algorithm the currently the fastest randomized algorithm for the general 3SAT problem.

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Notes

  1. 1.

    Throughout this paper, we use n, the number of variables of an input formula, as a size parameter. Following the standard convention on this topic, we ignore the polynomial factor for discussing the time complexity of algorithms, and by \({\widetilde{O}}(T(n))\) we denote O(T(n)p(n)) for some polynomial p.

  2. 2.

    In [2], the part of the algorithm \(\mathrm{HERTLI}\) corresponding to the statements 5–16 of Algorithm 2 is stated as algorithm OneCC (i.e., Algorithm 3 in [2]). On the other hand, we omit specifying it here and include it in Algorithm 2. In order to use algorithm numbering consistent with [2], we skip Algorithm 3 here and state \(\mathrm{GetInd2Clauses}\) as Algorithm 4. While \(\mathrm{DensePPSZ}_p\) and \(\mathrm{SparsePPSZ}\) correspond to procedures Dense (Algorithm 5) and Sparse (Algorithm 6) of [2], we modify their descriptions for the sake of our later explanation. As a whole, the procedure \(\mathrm{HERTLI}\) is essentially the same as Hertli’s algorithm stated in [2].

  3. 3.

    Due to some minor error in [2], the choice of parameters in [2] is not appropriate, which has been corrected in [3]. Here we use this corrected version.

References

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  8. Wahlström, M.: An algorithm for the SAT problem for formulae of linear length. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 107–118. Springer, Heidelberg (2005). https://doi.org/10.1007/11561071_12

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Authors and Affiliations

  1. School of Computing, Tokyo Institute of Technology, Tokyo, Japan

    Tong Qin & Osamu Watanabe

Authors
  1. Tong Qin
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  2. Osamu Watanabe
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Corresponding author

Correspondence to Tong Qin .

Editor information

Editors and Affiliations

  1. Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    M. Sohel Rahman

  2. National University of Singapore , Singapore, Singapore

    Wing-Kin Sung

  3. Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Ryuhei Uehara

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Qin, T., Watanabe, O. (2018). An Improvement of the Algorithm of Hertli for the Unique 3SAT Problem. In: Rahman, M., Sung, WK., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2018. Lecture Notes in Computer Science(), vol 10755. Springer, Cham. https://doi.org/10.1007/978-3-319-75172-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-75172-6_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-75171-9

  • Online ISBN: 978-3-319-75172-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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