Approximation Algorithm for the Balanced 2-Connected Bipartition Problem

  • Di Wu
  • Zhao Zhang
  • Weili Wu
  • Xiaohui Huang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8591)


For two positive integers m,k and a connected graph G = (V,E) with a nonnegative vertex weight function w, the balanced m-connected k-partition problem, denoted as BC m P k , is to find a partition of V into k disjoint nonempty vertex subsets (V 1,V 2,…,V k ) such that each G[V i ] (the subgraph of G induced by V i ) is m-connected, and min 1 ≤ i ≤ k {w(V i )} is maximized. In this paper, we study the BC 2 P 2 problem on 4-connected interval graphs. First, a 3/2-approximation algorithm is given. Then, assuming that w is integral, a fully polynomial time approximation scheme (FPTAS) is obtained. As far as we known, this is the first paper studying balanced connected partition problem with higher connectivity requirement on each part.


balanced m-connected k-partition interval graph pseudo-polynomial time algorithm FPTAS 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. The Macmillan Press, London (1976)zbMATHGoogle Scholar
  2. 2.
    Chataigner, F., Salgado, L.R.B., Wakabayashi, Y.: Approximation and inaproximability results on balanced connected partitions of graphs. Discrete Mathematics and Theoretical Computer Science 9, 177–192 (2007)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Chlebíková, J.: Approximating the maximally balanced connected partition problem in graphs. Information Processing Letters 60, 225–230 (1996)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Dyer, M., Frieze, A.: On the complexity of partitioning graphs into connected subgraphs. Discrete Applied Mathematics 10, 139–153 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Galbiati, G., Maffioli, F., Morzenti, A.: On the approximability of some maximum spanning tree problems. Theoretical Computer Science 181(1), 107–118 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to The Theory of NP-Completeness. Freeman, New York (1979)zbMATHGoogle Scholar
  7. 7.
    Györi, E.: On division of graph to connected subgraphs. In: Combinatoris (Proc. Fifth Hungarian Colloq., Koszthely, 1976). Colloq. Math. Soc. János Bolyai, vol. I, 18, pp. 485–494. North-Holland, Amsterdam (1978)Google Scholar
  8. 8.
    Lovász, L.: A homology theory for spanning trees of a graph. Acta Math. Acad. Sci. Hunger. 30, 241–251 (1977)CrossRefGoogle Scholar
  9. 9.
    Lucertini, M., Perl, Y., Simeone, B.: Most uniform path partitioning and its use in image processing. Discrete Applied Math. 42, 227–256 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Maravalle, M., Simeone, B., Naldini, R.: Clustering on trees. Comput. Statist. Data Anal. 24, 217–234 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Wu, B.Y.: Fully polynomial time approximation schemes for the max-min connected partition problem on interval graphs. Discrete Math. Algorithm. Appl. 04, 1250005 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Di Wu
    • 1
  • Zhao Zhang
    • 1
  • Weili Wu
    • 2
  • Xiaohui Huang
    • 1
  1. 1.College of Mathematics Physics and Information EngineeringZhejiang Normal UniversityZhejiangChina
  2. 2.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

Personalised recommendations