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A Simple and Fast Algorithm for Maximum Independent Set in 3-Degree Graphs

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WALCOM: Algorithms and Computation (WALCOM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5942))

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Abstract

We present a simple O *(1.0885n)-time algorithm for finding a maximum independent set in an n-vertex graph with degree bounded by 3, which improves most previous running time bounds obtained with far more complicated algorithms. In this paper, we use a nontraditional measure to analyze the problem size and some uniform branching rules to avoid tedious case analysis. Those techniques help us to design simple and fast algorithms with moderately complicated analysis.

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References

  1. Tarjan, R., Trojanowski, A.: Finding a maximum independent set. SIAM J. on Computing 6(3), 537–546 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  2. Jian, T.: An O(20.304n) algorithm for solving maximum independent set problem. IEEE Transactions on Computers 35(9), 847–851 (1986)

    Article  MATH  Google Scholar 

  3. Robson, J.: Algorithms for maximum independent sets. J. of Algorithms 7(3), 425–440 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  4. Robson, J.: Finding a maximum independent set in time O(2n/4). Technical Report 1251-01, LaBRI, Université Bordeaux I (2001)

    Google Scholar 

  5. Fomin, F.V., Grandoni, F., Kratsch, D.: Measure and conquer: a simple O(20.288n) independent set algorithm. In: SODA, pp. 18–25. ACM Press, New York (2006)

    Chapter  Google Scholar 

  6. Beigel, R.: Finding maximum independent sets in sparse and general graphs. In: SODA, pp. 856–857. ACM Press, New York (1999)

    Google Scholar 

  7. Chen, J., Kanj, I.A., Xia, G.: Labeled search trees and amortized analysis: Improved upper bounds for NP-hard problems. Algorithmica 43(4), 245–273 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Xiao, M.Y., Chen, J.E., Han, X.L.: Improvement on vertex cover and independent set problems for low-degree graphs. Chinese Journal of Computers 28(2), 153–160 (2005)

    MathSciNet  Google Scholar 

  9. Bourgeois, N., Escoffier, B., Paschos, V.T.: An O *(1.0977n) exact algorithm for max independent set in sparse graphs. In: Grohe, M., Niedermeier, R. (eds.) IWPEC 2008. LNCS, vol. 5018, pp. 55–65. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. Fomin, F.V., Høie, K.: Pathwidth of cubic graphs and exact algorithms. Inf. Process. Lett. 97(5), 191–196 (2006)

    Article  MATH  Google Scholar 

  11. Fürer, M.: A faster algorithm for finding maximum independent sets in sparse graphs. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 491–501. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Razgon, I.: A faster solving of the maximum independent set problem for graphs with maximal degree 3. In: Broersma, H., Dantchev, S.S., Johnson, M., Szeider, S. (eds.) ACiD. Texts in Algorithmics, vol. 7, pp. 131–142. King’s College, London (2006)

    Google Scholar 

  13. Razgon, I.: Faster computation of maximum independent set and parameterized vertex cover for graphs with maximum degree 3. J. of Discrete Algorithms 7(2), 191–212 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. Chen, J., Kanj, I., Xia, G.: Simplicity is beauty: Improved upper bounds for vertex cover. Technical Report TR05-008, School of CTI, DePaul University (2005)

    Google Scholar 

  15. Bourgeois, N., Escoffier, B., Paschos, V.T., van Rooij, J.M.M.: Fast algorithms for max independent set in graphs of small average degree. CoRR abs/0901.1563 (2009)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China

    Mingyu Xiao

Authors
  1. Mingyu Xiao
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology (BUET), 1000, Dhaka, Bangladesh

    Md. Saidur Rahman

  2. Graduate School of Engineering, Department of Information Engineering, Hiroshima University, Kagamiyama 1-4-1, 739-8527, Higashi-Hiroshima, Japan

    Satoshi Fujita

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Xiao, M. (2010). A Simple and Fast Algorithm for Maximum Independent Set in 3-Degree Graphs. In: Rahman, M.S., Fujita, S. (eds) WALCOM: Algorithms and Computation. WALCOM 2010. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11440-3_26

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  • DOI: https://doi.org/10.1007/978-3-642-11440-3_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11439-7

  • Online ISBN: 978-3-642-11440-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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