A Unifying View on Approximation and FPT of Agreement Forests

Whidden, Chris; Zeh, Norbert

doi:10.1007/978-3-642-04241-6_32

Cited by 41 publications

(67 citation statements)

References 18 publications

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“…Our definitions for the study about MAFs are consistent with those used in literature (Hein et al 1996;Bordewich and Semple 2005;Hallett and McCartin 2007;Whidden and Zeh 2009). A tree is a single-vertex tree if it consists of a single leaf vertex.…”

Section: Rooted X-trees X-forests and Agreement Forestsmentioning

confidence: 96%

“…A second 3-approximation algorithm presented in Rodrigues et al (2007) achieves a running time of O(n 2 ). Recently, Whidden and Zeh (2009), Whidden et al (2011) presented a linear-time approximation algorithm of ratio 3, which is the best known approximation algorithm for the Maximum Agreement Forest problem on two rooted binary phylogenetic trees.…”

Section: Introductionmentioning

confidence: 99%

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Improved approximation algorithm for maximum agreement forest of two rooted binary phylogenetic trees

Shi

Jie

et al. 2015

J Comb Optim

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Given two rooted binary phylogenetic trees with identical leaf label-set, the maximum agreement forest (MAF) problem asks for a largest common subforest of the two trees. This problem has been studied extensively in the literature, and has been known to be NP-complete and MAX SNP-hard. The previously best ratio of approximation algorithms for this problem is 3. In this paper, we make full use of the special relations among leaves in phylogenetic trees and present an approximation algorithm with ratio 2.5 for the MAF problem on two rooted binary phylogenetic trees.

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Section: Rooted X-trees X-forests and Agreement Forestsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Improved approximation algorithm for maximum agreement forest of two rooted binary phylogenetic trees

Shi

Jie

et al. 2015

J Comb Optim

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“…Although the SPR distance (rooted and unrooted) is NP-hard to compute [3,12], it is fixed-parameter tractable with respect to the distance in the rooted case [3]. In particular, one can determine in O(n)-time whether two rooted phylogenetic trees are adjacent in the rSPR graph (O(n 2 )-time for unrooted trees) using the algorithms of Whidden et al [42][43][44]46]. We applied this method comparing each of the m trees pairwise to identify adjacencies, requiring a total of O(m 2 n)-time (O(m 2 n 2 )-time in the unrooted case).…”

Section: Preliminariesmentioning

confidence: 99%

Ricci-Ollivier Curvature of the Rooted Phylogenetic Subtree-Prune-Regraft Graph

Whidden

Matsen

2015

2016 Proceedings of the Thirteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

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Statistical phylogenetic inference methods use tree rearrangement operations such as subtree-prune-regraft (SPR) to perform Markov chain Monte Carlo (MCMC) across tree topologies. These methods are known to mix quickly when sampling from the simple uniform distribution of trees but may become stuck in the local optima of multi-modal posterior distributions for real data induced by non-uniform likelihoods. The structure of the graph induced by tree rearrangement operations is an important determinant of the mixing properties of MCMC, motivating study of the underlying rSPR graph in greater detail.In this paper, we investigate the rSPR graph in a new way: by calculating Ricci-Ollivier curvature with respect to uniform and Metropolis-Hastings random walks. We confirm using simulation that mean access time distributions depend on distance, degree, and curvature, showing the relevance of these curvature results to stochastic tree search. These calculations require fast new algorithms for constructing and sampling these graphs, reducing the time required to compute an rSPR graph from O(m 2 n)-time to O(mn 3 ), where m is the (often large) number of trees in the graph and n their number of leaves, and reducing the time required to select an SPR neighbor of a tree uniformly at random to O(n) time. We then develop a closed form solution to characterize how the number of SPR neighbors of a tree changes after an SPR operation is applied to that tree. This gives bounds on the curvature, as well as a flatness-in-the-limit theorem indicating that paths of small topology changes are easy to traverse. However, we find that large topology changes (i.e. moving a large subtree) gives pairs of trees with negative curvature. Although these pairs of trees with negative curvature do not impede mixing in this simple well-connected space, they may manifest as bottlenecks in the much smaller * This work was funded by National Science Foundation award 1223057. Chris Whidden is a Simons Foundation Fellow of the Life Sciences Research Foundation.† Program in Computational Biology, Fred Hutchinson Cancer Research Center, Seattle, WA, USA 98109. {cwhidden,matsen}@fredhutch.org credible sets induced by phylogenetic posteriors with a likelihood function. This work extends our knowledge of the rSPR graph, in particular properties that are relevant for investigation of sampling the rSPR graph.

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“…This two-gene-tree case is closely related to computing the subtree prune and regraft (SPR) distance of two trees, a well-studied NP complete problem (Hein, et al, 1996;Bordewich and Semple, 2004) in phylogenetics. Nonetheless, there are several practical algorithms for the SPR distance problem (e.g., Wu, 2009;Whidden and Zeh, 2009). For the two-gene-tree case of the hybridization network problem, there are also several exact methods Wu and Wang, 2010;Albrecht et al, 2012).…”

Section: Wumentioning

confidence: 99%

“…This is essentially the main formulation used by many existing approaches to these two problems. The divide and conquer approach, developed in Whidden and Zeh (2009), and related approaches (Albrecht et al, 2012;Chen and Wang, 2013) are currently the best performing approaches for these two problems.…”

Section: Wumentioning

confidence: 99%

An Algorithm for Constructing Parsimonious Hybridization Networks with Multiple Phylogenetic Trees

2013

Journal of Computational Biology

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A phylogenetic network is a model for reticulate evolution. A hybridization network is one type of phylogenetic network for a set of discordant gene trees and ''displays'' each gene tree. A central computational problem on hybridization networks is: given a set of gene trees, reconstruct the minimum (i.e., most parsimonious) hybridization network that displays each given gene tree. This problem is known to be NP-hard, and existing approaches for this problem are either heuristics or making simplifying assumptions (e.g., work with only two input trees or assume some topological properties).In this article, we develop an exact algorithm (called PIRN C ) for inferring the minimum hybridization networks from multiple gene trees. The PIRN C algorithm does not rely on structural assumptions (e.g., the so-called galled networks). To the best of our knowledge, PIRN C is the first exact algorithm implemented for this formulation. When the number of reticulation events is relatively small (say, four or fewer), PIRN C runs reasonably efficient even for moderately large datasets. For building more complex networks, we also develop a heuristic version of PIRN C called PIRN CH . Simulation shows that PIRN CH usually produces networks with fewer reticulation events than those by an existing method.PIRN C and PIRN CH have been implemented as part of the software package called PIRN and is available online.

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A Unifying View on Approximation and FPT of Agreement Forests

Cited by 41 publications

References 18 publications

Improved approximation algorithm for maximum agreement forest of two rooted binary phylogenetic trees

Improved approximation algorithm for maximum agreement forest of two rooted binary phylogenetic trees

Ricci-Ollivier Curvature of the Rooted Phylogenetic Subtree-Prune-Regraft Graph

An Algorithm for Constructing Parsimonious Hybridization Networks with Multiple Phylogenetic Trees

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