Fixed Parameter Polynomial Time Algorithms for Maximum Agreement and Compatible Supertrees

Viet Tung Hoang & Wing-Kin Sung
Consider a set of labels $L$ and a set of trees ${mathcal T} = { {mathcal T}^{(1), {mathcal T}^{(2), ldots, {mathcal T}^{(k)$ where each tree ${mathcal T}^{(i)$ is distinctly leaf-labeled by some subset of $L$. One fundamental problem is to find the biggest tree (denoted as supertree) to represent $mathcal T}$ which minimizes the disagreements with the trees in ${mathcal T}$ under certain criteria. This problem finds applications in phylogenetics, database, and data mining....