# Constructing the Simplest Possible Phylogenetic Network from Triplets

@article{Iersel2009ConstructingTS, title={Constructing the Simplest Possible Phylogenetic Network from Triplets}, author={Leo van Iersel and Steven M. Kelk}, journal={Algorithmica}, year={2009}, volume={60}, pages={207-235} }

A phylogenetic network is a directed acyclic graph that visualizes an evolutionary history containing so-called reticulations such as recombinations, hybridizations or lateral gene transfers. Here we consider the construction of a simplest possible phylogenetic network consistent with an input set T, where T contains at least one phylogenetic tree on three leaves (a triplet) for each combination of three taxa. To quantify the complexity of a network we consider both the total number of…

## 52 Citations

NetCombin: An algorithm for optimal level-k network construction from triplets

- Computer SciencebioRxiv
- 2020

In this research, a new algorithm called Netcombin is introduced to construct an optimal network which is consistent with input triplets, based on binarization and expanding processes.

Netcombin: An algorithm for constructing optimal phylogenetic network from rooted triplets

- Computer SciencePloS one
- 2020

The experimental results on simulated data obtained from biologically generated sequences data indicate that by considering the trade-off between speed and precision, the Netcombin outperforms the others.

Encoding and Constructing 1-Nested Phylogenetic Networks with Trinets

- Biology, Computer ScienceAlgorithmica
- 2012

This work shows that for a special, well-studied type of phylogenetic network, the trinets displayed by a 1-nested network always encode the network, which uses phylogenetic networks on 3-element subsets of a set, or trinet, rather than triplets.

Constructing a Minimum phylogenetic Network from a Dense triplet Set

- MathematicsJ. Bioinform. Comput. Biol.
- 2012

For any k fixed, it is possible to construct a level-k network having the minimum number of hybrid vertices and consistent with T, if there is any, in time O(T(k+1)n([4k/3]+1)).

On the Elusiveness of Clusters

- Computer ScienceIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2012

It is proved that, for every fixed k ≥ 0, it is polynomial-time solvable to construct a phylogenetic network with level equal to k representing a cluster set, or to determine that no such network exists.

TripNet: A Method for Constructing Rooted Phylogenetic Networks from Rooted Triplets

- Computer SciencePloS one
- 2014

This paper presents a heuristic algorithm called TripNet, which tries to construct a rooted phylogenetic network with the minimum number of reticulation nodes from an arbitrary set of rooted triplets, and proves some theorems to clarify the performance of the algorithm.

A Practical Algorithm for Reconstructing Level-1 Phylogenetic Networks

- Computer ScienceIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2011

An efficient, practical algorithm for reconstructing level-1 phylogenetic networks-a type of network slightly more general than a phylogenetic tree-from triplets that is able to construct networks consistent with a high percentage of input triplets, even when theseinput triplets are affected by a low to moderate level of noise.

Level-k Phylogenetic Network can be Constructed from a Dense Triplet Set in Polynomial Time

- Computer Science
- 2009

A complete answer to the general case of phylogenetic networks consistent with $\mathcal{T}$ is given and a special property of SN-sets in a level-k network is used, which can also find the level- k network with the minimum number of reticulations in polynomial time.

Hierarchies from Lowest Stable Ancestors in Nonbinary Phylogenetic Networks

- Computer ScienceJ. Classif.
- 2019

A novel approach to understanding the structure of networks that are not necessarily binary by defining the concept of a closed set and showing that the collection of closed sets of a network forms a hierarchy, and that this hierarchy can be deduced from either the subtrees or subnetworks on all 3-subsets.

Phylogenetic networks do not need to be complex: using fewer reticulations to represent conflicting clusters

- BiologyBioinform.
- 2010

The new Cass algorithm is presented, which is a generalization of phylogenetic trees that can combine any set of clusters into a phylogenetic network, and it is shown that the networks constructed by Cass are usually simpler than Networks constructed by other available methods.

## References

SHOWING 1-10 OF 38 REFERENCES

Uniqueness, Intractability and Exact Algorithms: Reflections on Level-k Phylogenetic Networks

- Computer ScienceJ. Bioinform. Comput. Biol.
- 2009

This work gives an exact algorithm for constructing level-1 networks consistent with a maximum number of input triplets, and proves that for all k > or = 1 it is NP-hard to construct a level-k network consistent with allinput triplets.

Inferring phylogenetic relationships avoiding forbidden rooted triplets

- BiologyAPBC
- 2005

This paper considers the problem of constructing a phylogenetic tree/network which is consistent with all of the rooted triplets in a given set C and none of the Root Triplets in another given set F and provides some efficient exact and approximation algorithms for a number of biologically meaningful variants of the problem.

Constructing Level-2 Phylogenetic Networks from Triplets

- Computer ScienceIEEE ACM Trans. Comput. Biol. Bioinform.
- 2009

This work shows that, assuming density, it is tractable to construct plausible evolutionary histories from input triplets even when such histories are heavily non-tree like, and strengthens the case for the use of triplet-based methods in the construction of phylogenetic networks.

Constructing Level-2 Phylogenetic Networks from Triplets

- Computer ScienceIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2009

It is shown that, assuming density, it is tractable to construct plausible evolutionary histories from input triplets even when such histories are heavily nontree-like, which further strengthens the case for the use of triplet-based methods in the construction of phylogenetic networks.

Optimal, Efficient Reconstruction of Phylogenetic Networks with Constrained Recombination

- Computer Science, BiologyJ. Bioinform. Comput. Biol.
- 2004

It is proved that if there is a galled-tree, then the one produced by the algorithm minimizes the number of recombinations over all phylogenetic networks for the data, even allowing multiple-crossover recombinations.

Inferring a Level-1 Phylogenetic Network from a Dense Set of Rooted Triplets

- Computer ScienceCOCOON
- 2004

An O(n 5)-time algorithm for finding the set of all phylogenetic networks having a single hybrid node attached to exactly one leaf (and having no other hybrid nodes) that are consistent with a given dense set of rooted triplets.

Computing the maximum agreement of phylogenetic networks

- Computer ScienceTheor. Comput. Sci.
- 2005

Worst-case optimal approximation algorithms for maximizing triplet consistency within phylogenetic networks

- MathematicsJ. Discrete Algorithms
- 2010

Constructing a Smallest Refining Galled Phylogenetic Network

- Computer ScienceRECOMB
- 2005

Two new efficient algorithms for inferring a phylogenetic network from a set of gene trees of arbitrary degrees named RGNet and RGNet are presented and it is shown that these methods outperform the other existing methods neighbor-joining, NeighborNet, and SpNet.

Algorithms for combining rooted triplets into a galled phylogenetic network

- Computer ScienceSODA '05
- 2005

It is proved that the problem of determining whether a given set of rooted triplets can be merged without conflicts into a galled phylogenetic network, and if so, constructing such a network, is NP-hard if extended to non-dense inputs.