On the parameterized complexity of some optimization problems related to multiple-interval graphs

  • Authors:

  • Minghui Jiang

  • Affiliations:

  • -

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

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^(^k^l^o^g^k^)}@?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 solution.