# Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

# Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network

• Jesper Jansson
• Wing-Kin Sung
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_92-2

## Years and Authors of Summarized Original Work

2006; Jansson, Sung

2006; Jansson, Nguyen, Sung

2006; He, Huynh, Jansson, Sung

2010; Byrka, Gawrychowski, Huber, Kelk

2011; van Iersel, Kelk

## Problem Definition

A phylogenetic tree is a binary, rooted, unordered tree whose leaves are distinctly labeled. A phylogenetic network is a generalization of a phylogenetic tree formally defined as a rooted, connected, directed acyclic graph in which (1) each node has outdegree at most 2; (2) each node has indegree 1 or 2, except the root node which has indegree 0; (3) no node has both indegree 1 and outdegree 1; and (4) all nodes with outdegree 0 are labeled by elements from a finite set L in such a way that no two nodes are assigned the same label. Nodes of outdegree 0 are referred to as leaves and are identified with their corresponding elements in L. Nodes with indegree 2 are called reticulation nodes. For any phylogenetic network N, let $$\mathcal{U}(N)$$

## Keywords

Dense set, Galled phylogenetic network, Phylogenetic tree, Polynomial-time approximation algorithm, Rooted triplet
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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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