Solving the Maximum Agreement SubTree and the Maximum Compatible Tree Problems on Many Bounded Degree Trees

  • Sylvain Guillemot
  • François Nicolas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4009)


Given a set of leaf-labeled trees with identical leaf sets, the well-known Maximum Agreement SubTree problem (MAST) consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. Its variant called Maximum Compatible Tree (MCT) is less stringent, as it allows the input trees to be refined. Both problems are of particular interest in computational biology, where trees encountered have often small degrees.

In this paper, this paper, we study the parameterized complexity of MAST and MCT with respect to the maximum degree, denoted D, of the input trees. While MAST is polynomial for bounded D [1,6,3], we show that MAST is W[1]-hard with respect to parameter D. Moreover, relying on recent advances in parameterized complexity we obtain a tight lower bound: while MAST can be solved in O(N \(^{O({\it D})}\)) time where N denotes the input length, we show that an O(N \(^{o({\it D})}\)) bound is not achievable, unless SNP ⊆ SE. We also show that MCT is W[1]-hard with respect to D, and that MCT cannot be solved in \(O\big(N^{o(2^{D/2})}\big)\) time, unless SNP ⊆ SE.


Maximum Degree Parameterized Complexity Mast Problem Input Tree Leaf Label 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sylvain Guillemot
    • 1
  • François Nicolas
    • 1
  1. 1.LIRMMMontpellierFrance

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