On the Parameterized Complexity of Some Optimization Problems Related to Multiple-Interval Graphs

  • Minghui Jiang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6129)


We show that for any constant t ≥ 2, k -Independent Set and k -Dominating Set in t-track interval graphs are W[1]-hard. This settles an open question recently raised by Fellows, Hermelin, Rosamond, and Vialette. We also give an FPT algorithm for k -Clique in t-interval graphs, parameterized by both k and t, with running time max { t O(k), 2 O(klogk) } ·poly(n), where n is the number of vertices in the graph. This slightly improves the previous FPT algorithm by Fellows, Hermelin, Rosamond, and Vialette. Finally, we use the W[1]-hardness of k -Independent Set in t-track interval graphs to obtain the first parameterized intractability result for a recent bioinformatics problem called Maximal Strip Recovery (MSR). We show that MSR-d is W[1]-hard for any constant d ≥ 4 when the parameter is either the total length of the strips, or the total number of adjacencies in the strips, or the number of strips in the optimal solution.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Minghui Jiang
    • 1
  1. 1.Department of Computer ScienceUtah State UniversityLoganUSA

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