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An Improved Parameterized Algorithm for the Minimum Node Multiway Cut Problem

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Abstract

The parameterized node multiway cut problem is for a given graph to find a separator of size bounded by k whose removal separates a collection of terminal sets in the graph. In this paper, we develop an O(k4k n 3) time algorithm for this problem, significantly improving the previous algorithm of time \(O(4^{k^{3}}n^{5})\) for the problem. Our result gives the first polynomial time algorithm for the minimum node multiway cut problem when the separator size is bounded by O(log n).

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References

  1. Boykov, Y., Veksler, O., Zabih, R.: Markov random fields with efficient approximations. In: Proc. IEEE Conference on Computer Vision and Pattern Recognition, pp. 648–655, 1998

  2. Calinescu, G., Karloff, H., Rabani, Y.: An improved approximation algorithm for multiway cut. J. Comput. Syst. Sci. 60, 564–574 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chartrand, G., Lesniak, L.: Graphs & Digraphs, 2nd edn. Wadsworth/Cole Mathematics Series, Belmont (1986)

    Google Scholar 

  4. Chen, J., Liu, Y., Lu, S., O’Sullivan, B., Razgon, I.: A fixed-parameter algorithm for the directed feedback vertex set problem. Manuscript (2007)

  5. Cong, J., Labio, W., Shivakumar, N.: Multi-way VLSI circuit partitioning based on dual net representation. In: Proc. IEEE International Conference on Computer-Aided Design, pp. 56–62, 1994

  6. Cunningham, W.: The optimal multiterminal cut problem. DIMACS Ser. Discrete Math. Theor. Comput. Sci. 5, 105–120 (1991)

    MathSciNet  Google Scholar 

  7. Dahlhaus, E., Johnson, D., Papadimitriou, C., Seymour, P., Yannakakis, M.: The complexity of multiterminal cuts. SIAM J. Comput. 23, 864–894 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  8. Downey, R., Fellows, M.: Fixed-parameter tractability and completeness I: basic results. SIAM J. Comput. 24, 873–921 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Downey, R., Fellows, M.: Parameterized Complexity. Monograph in Computer Science. Springer, New York (1999)

    Google Scholar 

  10. Ford, L. Jr., Fulkerson, D.: Flows in Networks. Princeton University Press, Princeton (1962)

    MATH  Google Scholar 

  11. Karger, D., Levine, M.: Finding maximum flows in undirected graphs seems easier than bipartite matching. In: Proc. 30th Annual ACM Symposium on Theory of Computing, pp. 69–78, 1998

  12. Karger, D., Klein, P., Stein, C., Thorup, M., Young, N.: Rounding algorithms for a geometric embedding of minimum multiway cut. In: Proc. 31th Annual ACM Symposium on Theory of Computing, pp. 668–678, 1999

  13. Marx, D.: Parameterized graph separation problems. Theor. Comput. Sci. 351, 394–406 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Naor, J., Zosin, L.: A 2-approximation algorithm for the directed multiway cut problem. SIAM J. Comput. 31, 477–482 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Stone, H.: Multiprocessor scheduling with the aid of network flow algorithms. IEEE Trans. Softw. Eng. 3, 85–93 (1977)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Texas A&M University, College Station, TX, 77843, USA

    Jianer Chen, Yang Liu & Songjian Lu

Authors
  1. Jianer Chen
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  2. Yang Liu
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  3. Songjian Lu
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Corresponding author

Correspondence to Songjian Lu.

Additional information

A preliminary version of this paper was presented at The 10th Workshop on Algorithms and Data Structures (WADS 2007).

This work was supported in part by the National Science Foundation under the Grants CCR-0311590 and CCF-0430683.

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Chen, J., Liu, Y. & Lu, S. An Improved Parameterized Algorithm for the Minimum Node Multiway Cut Problem. Algorithmica 55, 1–13 (2009). https://doi.org/10.1007/s00453-007-9130-6

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  • DOI: https://doi.org/10.1007/s00453-007-9130-6

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