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Compatibility of unrooted phylogenetic trees is FPT. (English) Zbl 1086.68097
Summary: A collection of \(T_{1},T_{2},\cdots,T_{k}\) of unrooted, leaf labelled (phylogenetic) trees, all with different leaf sets, is said to be compatible if there exists a tree \(T\) such that each tree \(T_{i}\) can be obtained from \(T\) by deleting leaves and contracting edges. Determining compatibility is NP-hard, and the fastest algorithm to date has worst case complexity of around \(\Omega(n^{k})\) time, \(n\) being the number of leaves. Here, we present an O\((nf(k))\) algorithm, proving that compatibility of unrooted phylogenetic trees is fixed parameter tractable (FPT) with respect to the number \(k\) of trees.

MSC:
68R10 Graph theory (including graph drawing) in computer science
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