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A 7/6-Approximation Algorithm for the Max-Min Connected Bipartition Problem on Grid Graphs

  • Bang Ye Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)

Abstract

For a given graph with nonnegative weights on nodes, the max-min connected bipartition problem looks for a way to partition the graph into two connected subgraphs such that the minimum weight of the two subgraphs is maximized. In this paper, we give a polynomial time 7/6-approximation algorithm for grid graphs. The approximation ratio is currently the best result achieved in polynomial time.

Keywords

algorithm approximation algorithm non-separating path connected partition grid graph 

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References

  1. 1.
    Becker, R., Lari, I., Lucertini, M., Simeone, B.: Max-min partitioning of grid graphs into connected components. Networks 32, 115–125 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Becker, R., Lari, I., Lucertini, M., Simeone, B.: A polynomial-time algorithm for max-min partitioning of ladders. Theor. Comput. Syst. 34, 353–374 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bender, M.A., Farach-Colton, M., Pemmasani, G., Skiena, S., Sumazin, P.: Lowest common ancestors in trees and directed acyclic graphs. J. Algorithms 57, 75–94 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chataigner, F., Salgado, L.R.B., Wakabayashi, Y.: Approximation and Inaproximability results on balanced connected partitions of graphs. Discret. Math. Theor. Comput. Sci. 9, 177–192 (2007)zbMATHGoogle Scholar
  5. 5.
    Chlebíková, J.: Approximating the maximally balanced connected partition problem in graphs. Inf. Process. Lett. 60, 225–230 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Even, S., Tarjan, R.E.: Computing an st-numbering. Theor. Comput. Sci. 2, 339–344 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34, 209–221 (1987)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lovász, L.: A homology theory for spanning trees of a graph. Acta Math. Acad. Sci. Hunger 30, 241–251 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Perl, Y., Schach, S.: Max-min tree partitioning. J. ACM 28, 5–15 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    West, D.B.: Introduction to Graph Theory 2001. Prentice Hall (2001)Google Scholar
  11. 11.
    Wu, B.Y.: The minimum non-separating path and the balanced connected bipartition on grid graphs, arXiv:1105.5915v1 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Bang Ye Wu
    • 1
  1. 1.National Chung Cheng UniversityChiaYiTaiwan, R.O.C.

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