Efficient Algorithms for Computing the Triplet and Quartet Distance Between Trees of Arbitrary Degree

Brodal, Gerth Stølting; Fagerberg, Rolf; Mailund, Thomas; Pedersen, Christian N. S.; Sand, Andreas

doi:10.1137/1.9781611973105.130

Cited by 27 publications

(69 citation statements)

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“…We present an implementation, evaluation and improvements to the algorithms in [4]. The algorithm in [4] for computing the triplet distance between two trees of arbitrary degree uses time O(n · 1 Source code at http://cs.au.dk/~mailund/qdist.html 2 Source code at http://birc.au.dk/software/qdist/ lg n) and space O(n · min(d 1 , lg n)).…”

Section: Our Resultsmentioning

confidence: 99%

“…The algorithm in [4] for computing the triplet distance between two trees of arbitrary degree uses time O(n · 1 Source code at http://cs.au.dk/~mailund/qdist.html 2 Source code at http://birc.au.dk/software/qdist/ lg n) and space O(n · min(d 1 , lg n)). Runtime and memory usage results for this algorithm are presented in Sect.…”

Section: Our Resultsmentioning

confidence: 99%

“…Bansal et al [1] gave an algorithm for calculating the triplet distance of arbitrary degree trees in time O(n 2 ). Recently an O(n lg 2 n) algorithm calculating the triplet distance for binary trees was given by Sand et al [13], and an algorithm calculating the quartet distance in time O(dn lg n), as well as the triplet distance of two trees of arbitrary degree in time O(n lg n) was given by Brodal et al [4]. Tables 1 and 2 summarize the theoretical work on triplet and quartet distance compu-Year Reference Runtime Arb.…”

Section: Previous Workmentioning

confidence: 99%

“…O(n 4 ) 1996 [6] O(n 2 ) 2011 [1] O(n 2 ) 2013 [13] O(n · lg 2 n) 2013 [4] O(n · lg n) Naive tations. The last column in the tables indicates if the algorithms also work for trees of arbitrary degree.…”

Section: Naivementioning

confidence: 99%

“…The last column in the tables indicates if the algorithms also work for trees of arbitrary degree. An experimental evaluation of the algorithms in [4] is the subject of this paper.…”

Section: Naivementioning

confidence: 99%

See 4 more Smart Citations

On the Scalability of Computing Triplet and Quartet Distances

Holt¹,

Johansen²,

Brodal³

2013

2014 Proceedings of the Sixteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

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In this paper we present an experimental evaluation of the algorithms by Brodal et al. [SODA 2013] for computing the triplet and quartet distance measures between two leaf labelled rooted and unrooted trees of arbitrary degree, respectively. The algorithms count the number of rooted tree topologies over sets of three leaves (triplets) and unrooted tree topologies over four leaves (quartets), respectively, that have different topologies in the two trees.The algorithms by Brodal et al. maintain a long sequence of variables (hundreds for quartets) for counting different cases to be considered by the algorithm, making it unclear if the algorithms would be of theoretical interest only. In our experimental evaluation of the algorithms the typical overhead per node is about 2 KB and 10 KB per node in the input trees for triplet and quartet computations, respectively. This allows us to compute the distance measures for trees with up to millions of nodes. The limiting factor is the amount of memory available. With 31 GB of memory all our input instances can be solved within a few minutes.In the algorithm by Brodal et al. a few choices were made, where alternative solutions possibly could improve the algorithm, in particular for quartet distance computations. For quartet computations we expand the algorithm to also consider alternative computations, and make two observations: First we observe that the running time can be improved from O(max(d1, d2)where n is the number of leaves in the two trees, and d1 and d2 are the maximum degrees of the nodes in the two trees, respectively. Secondly, by taking a different approach to counting the number of disagreeing quartets we can reduce the number of calculations needed to calculate the quartet distance, improving both the running time and the space requirement by our algorithm by a constant factor.

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Section: Our Resultsmentioning

confidence: 99%

Section: Our Resultsmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

Section: Naivementioning

confidence: 99%

“…The last column in the tables indicates if the algorithms also work for trees of arbitrary degree. An experimental evaluation of the algorithms in [4] is the subject of this paper.…”

Section: Naivementioning

confidence: 99%

See 3 more Smart Citations

On the Scalability of Computing Triplet and Quartet Distances

Holt¹,

Johansen²,

Brodal³

2013

2014 Proceedings of the Sixteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

Self Cite

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Comparison of phylogenetic trees defined on different but mutually overlapping sets of taxa: A review

Li,

Koshkarov,

Tahiri

2024

Ecology and Evolution

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Phylogenetic trees represent the evolutionary relationships and ancestry of various species or groups of organisms. Comparing these trees by measuring the distance between them is essential for applications such as tree clustering and the Tree of Life project. Many distance metrics for phylogenetic trees focus on trees defined on the same set of taxa. However, some problems require calculating distances between trees with different but overlapping sets of taxa. This study reviews state‐of‐the‐art distance measures for such trees, covering six major approaches, including the constraint‐based Robinson–Foulds (RF) distance RF(−), the completion‐based RF(+), the generalized RF (GRF), the dissimilarity measure, the vectorial tree distance, and the geodesic distance in the extended Billera‐Holmes‐Vogtmann tree space. Among these, three RF‐based methods, RF(−), RF(+), and GRF, were examined in detail on generated clusters of phylogenetic trees defined on different but mutually overlapping sets of taxa. Additionally, we reviewed nine related techniques, including leaf imputation methods, the tree edit distance, and visual comparison. A comparison of the related distance measures, highlighting their principal advantages and shortcomings, is provided. This review offers valuable insights into their applicability and performance, guiding the appropriate use of these metrics based on tree type (rooted or unrooted) and information type (topological or branch lengths).

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Computing the Rooted Triplet Distance Between Phylogenetic Networks

Jansson

Mampentzidis

Rajaby

et al. 2019

Lecture Notes in Computer Science

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The rooted triplet distance measures the structural dissimilarity of two phylogenetic trees or phylogenetic networks by counting the number of rooted phylogenetic trees with exactly three leaf labels (called rooted triplets, or triplets for short) that occur as embedded subtrees in one, but not both, of them. Suppose that N 1 = (V 1 , E 1 ) and N 2 = (V 2 , E 2 ) are phylogenetic networks over a common leaf label set of size n, that N i has level k i and maximum in-degree d i for i ∈ {1, 2} , and that the networks' out-degrees are unbounded. Write. Previous work has shown how to compute the rooted triplet distance between N 1 and N 2 in O(n log n) time in the special case k ≤ 1 . For k > 1 , no efficient algorithms are known; applying a classic method from 1980 by Fortune et al. in a direct way leads to a running time of Ω(N 6 n 3 ) and the only existing non-trivial algorithm imposes restrictions on the networks' in-and outdegrees (in particular, it does not work when non-binary vertices are allowed). In this article, we develop two new algorithms with no such restrictions. Their running times are O(N 2 M + n 3 ) and O(M + Nk 2 d 2 + n 3 ) , respectively. We also provide implementations of our algorithms, evaluate their performance on simulated and real datasets, and make some observations on the limitations of the current definition of the rooted triplet distance in practice. Our prototype implementations have been packaged into the first publicly available software for computing the rooted triplet distance between unrestricted networks of arbitrary levels.

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Efficient Algorithms for Computing the Triplet and Quartet Distance Between Trees of Arbitrary Degree

Cited by 27 publications

References 9 publications

On the Scalability of Computing Triplet and Quartet Distances

On the Scalability of Computing Triplet and Quartet Distances

Comparison of phylogenetic trees defined on different but mutually overlapping sets of taxa: A review

Computing the Rooted Triplet Distance Between Phylogenetic Networks

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