Parameterized Graph Cleaning Problems

  • Dániel Marx
  • Ildikó Schlotter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5344)


We investigate the Induced Subgraph Isomorphism problem with non-standard parametrization, where the parameter is the difference |V(G)| − |V(H)| with H and G being the smaller and the larger input graph, respectively. Intuitively, we can interpret this problem as “cleaning” the graph G, regarded as a pattern containing extra vertices indicating errors, in order to obtain the graph H representing the original pattern. We show fixed-parameter tractability of the cases where both H and G are planar and H is 3-connected, or H is a tree and G is arbitrary.


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  1. 1.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The design and analysis of computer algorithms. Addison-Wesley, Reading (1974)MATHGoogle Scholar
  2. 2.
    Bodlaender, H.: On disjoint cycles. Int. J. Found. Comput. Sci. 5, 59–68 (1994)CrossRefMATHGoogle Scholar
  3. 3.
    Cai, L., Chan, S.M., Chan, S.O.: Random separation: a new method for solving fixed-cardinality optimization problems. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 239–250. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Chen, Y., Flum, J.: On parameterized path and chordless path problems. In: 22nd Annual IEEE Conference on Computational Complexity, pp. 250–263 (2007)Google Scholar
  5. 5.
    Díaz, J., Thilikos, D.M.: Fast FPT-algorithms for cleaning grids. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 361–371. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Diestel, R.: Graph Theory. Springer, Berlin (2000)MATHGoogle Scholar
  7. 7.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  8. 8.
    Eppstein, D.: Subgraph isomorphism in planar graphs and related problems. J. Graph Algorithms Appl. 3(3), 1–27 (1999)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)MATHGoogle Scholar
  10. 10.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)MATHGoogle Scholar
  11. 11.
    Hajiaghayi, M.T., Nishimura, N.: Subgraph isomorphism, log-bounded fragmentation and graphs of (locally) bounded treewidth. J. Comput. Syst. Sci. 73(5), 755–768 (2007)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Hopcroft, J.E., Tarjan, R.E.: Dividing a graph into triconnected components. SIAM J. Computing 2(3), 135–158 (1973)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Hopcroft, J.E., Tarjan, R.E.: Efficient planarity testing. J. Assoc. Comput. Mach. 21, 549–568 (1974)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Lingas, A.: Subgraph isomorphism for biconnected outerplanar graphs in cubic time. Theoret. Comput. Sci. 63(3), 295–302 (1989)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Marx, D., Schlotter, I.: Obtaining a planar graph by vertex deletion. In: Brandstädt, A., Kratsch, D., Müller, H. (eds.) WG 2007. LNCS, vol. 4769, pp. 292–303. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Matula, D.: Subtree isomorphism in O(n 5/2). Ann. Discrete Math. 2, 91–106 (1978)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Dániel Marx
    • 1
  • Ildikó Schlotter
    • 1
  1. 1.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsBudapestHungary

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