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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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##### References:
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