# Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

# Maximum Agreement Supertree

• Jesper Jansson
• Wing-Kin Sung
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_222-2

## Years and Authors of Summarized Original Work

2007; Berry, Nicolas

2010; Guillemot, Berry

2011; Hoang, Sung

## Problem Definition

A phylogenetic tree is a rooted, unordered tree whose leaves are distinctly labeled and whose internal nodes have degree at least two. By distinctly labeled, we mean that no two leaves in the tree have the same label. Let T be a phylogenetic tree with a leaf label set S. For any subset S′ of S, the topological restriction of T to S′ (denoted by T | S′) is the tree obtained from T by deleting all nodes which are not on any path from the root to a leaf in S′ along with their incident edges and then contracting every edge between a node having just one child and its child. See Fig. 1 for an illustration. For any phylogenetic tree T, denote its set of leaf labels by Λ(T).

## Keywords

Phylogenetic tree, Maximum agreement supertree, Rooted triplet, NP-hardness, Fixed-parameter tractability
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## Notes

### Acknowledgements

JJ was funded by the Hakubi Project at Kyoto University and KAKENHI grant number 26330014.

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