eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2008-02-06
361
372
10.4230/LIPIcs.STACS.2008.1357
article
Fixed Parameter Polynomial Time Algorithms for Maximum Agreement and Compatible Supertrees
Hoang, Viet Tung
Sung, Wing-Kin
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. In this paper, we focus
on two particular supertree problems, namely, the maximum agreement
supertree problem (MASP) and the maximum compatible supertree
problem (MCSP). These two problems are known to be NP-hard for $k
geq 3$. This paper gives the first polynomial time algorithms for
both MASP and MCSP when both $k$ and the maximum degree $D$ of the
trees are constant.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol001-stacs2008/LIPIcs.STACS.2008.1357/LIPIcs.STACS.2008.1357.pdf
Maximum agreement supertree
maximum compatible supertree