On the agreement of many trees
Information Processing Letters
On the complexity of comparing evolutionary trees
Discrete Applied Mathematics - Special volume on computational molecular biology
Maximum Agreement Subtree in a Set of Evolutionary Trees: Metrics and Efficient Algorithms
SIAM Journal on Computing
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
WABI '01 Proceedings of the First International Workshop on Algorithms in Bioinformatics
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Linear FPT reductions and computational lower bounds
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Parameterized Complexity
On the approximability of the Maximum Agreement SubTree and Maximum Compatible Tree problems
Discrete Applied Mathematics
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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.