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Consider a set of labels $L$ and a set of trees ${\mathcal T} = \{{\mathcalT}^{(1), {\mathcal T}^{(2), ..., {\mathcal T}^{(k) \$ where each tree${\mathcal T}^{(i)$ is distinctly leaf-labeled by some subset of $L$. Onefundamental problem is to find the biggest tree (denoted as supertree) torepresent $\mathcal T}$ which minimizes the disagreements with the trees in${\mathcal T}$ under certain criteria. This problem finds applications inphylogenetics, database, and data mining. In this paper, we focus on twoparticular supertree problems, namely, the maximum agreement supertree problem(MASP) and the maximum compatible supertree problem (MCSP). These two problemsare known to be NP-hard for $k \geq 3$. This paper gives the first polynomialtime algorithms for both MASP and MCSP when both $k$ and the maximum degree $D$of the trees are constant.

Fixed Parameter Polynomial Time Algorithms for Maximum Agreement and Compatible Supertrees