We present new and improved approximation and FPT algorithms for computing rooted and unrooted maximum agreement forests (MAFs) of pairs of phylogenetic trees. Their sizes correspond to the subtree-prune-and-regraft distances and the tree-bisection-and-reconnection distances of the trees, respectively. We also provide the first bounded search tree FPT algorithm for computing rooted maximum acyclic agreement forests (MAAFs) of pairs of phylogenetic trees, whose sizes are the hybridization numbers of these pairs of trees. These distance metrics are essential tools for understanding reticulate evolution.
Numerous heuristic approaches for computing SPR distances have also been proposed. LatTrans by Hallet and Lagergen @cite_19 models lateral gene transfer events by a restricted version of rooted SPR operations, considering two ways in which the trees can differ. It computes the exact distance under this restricted metric in @math time. HorizStory by Macleod et al. @cite_3 supports multifurcating trees but does not consider SPR operations where the pruned subtree contains more than one leaf. EEEP by Beiko and Hamilton @cite_0 performs a breadth-first SPR search on a rooted start tree but performs unrooted comparisons between the explored trees and an unrooted reference tree. The distance returned is not guaranteed to be exact, due to optimizations and heuristics that limit the scope of the search, although EEEP provides options to compute the exact unrooted SPR distance with no nontrivial bound on the running time. More recently, RiataHGT by Nakhleh et al. @cite_33 computes an approximation of the SPR distance between rooted multifurcating trees in polynomial time.
@cite_0 @cite_19 @cite_33 @cite_3
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We improve on earlier FPT algorithms for computing a rooted maximum agreement forest (MAF) or a maximum acyclic agreement forest (MAAF) of a pair of phylogenetic trees. Their sizes give the subtree-prune-and-regraft (SPR) distance and the hybridization number of the trees, respectively. We introduce new branching rules that reduce the running time of the algorithms from O(3kn) and O(3kn logn) to O(2.42kn) and O(2.42kn logn), respectively. In practice, the speed up may be much more than predicted by the worst-case analysis. We confirm this intuition experimentally by computing MAFs for simulated trees and trees inferred from protein sequence data. We show that our algorithm is orders of magnitude faster and can handle much larger trees and SPR distances than the best previous methods, treeSAT and sprdist. Statistical phylogenetic inference methods use tree rearrangement operations such as subtree–prune–regraft (SPR) to perform Markov chain Monte Carlo (MCMC) across tree topologies. The structure of the graph induced by tree rearrangement operations is an important determinant of the mixing properties of MCMC, motivating the study of the underlying SPR graph in greater detail. In this paper, we investigate the SPR graph of rooted trees (rSPR graph) in a new way: by calculating the Ricci–Ollivier curvature with respect to uniform and Metropolis–Hastings random walks. This value quantifies the degree to which a pair of random walkers from specified points move towards each other; negative curvature means that they move away from one another on average, while positive curvature means that they move towards each other. In order to calculate this curvature, we develop fast new algorithms for rSPR graph computation. We then develop formulas characterizing how the number of rSPR neighbors of a tree changes after an rSPR operation is applied to that tree. These give 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) give pairs of trees with negative curvature. We show using simulation that mean access time distributions depend on distance, degree, and curvature, demonstrating the relevance of these results to stochastic tree search. Motivation: Subtree prune and regraft (SPR) is one kind of tree rearrangements that has seen applications in solving several computational biology problems. The minimum number of rooted SPR (rSPR) operations needed to transform one rooted binary tree to another is called the rSPR distance between the two trees. Computing the rSPR distance has been actively studied in recent years. Currently, there is a lack of practical software tools for computing the rSPR distance for relatively large trees with large rSPR distance. Results: In this article, we present a simple and practical method that computes the exact rSPR distance with integer linear programming. By applying this new method on several simulated and real biological datasets, we show that our new method outperforms existing software tools in term of accuracy and ef.ciency. Our experimental results indicate that our method can compute the exact rSPR distance for many large trees with large rSPR distance. Availability: A software tool, SPRDist, is available for download from the web page: http: www.engr.uconn.edu ywu. Contact: ywu@engr.uconn.edu This paper proposes a tree kernel with contextsensitive structured parse tree information for relation extraction. It resolves two critical problems in previous tree kernels for relation extraction in two ways. First, it automatically determines a d ynamic context-sensitive tree span for relation extraction by extending the widely -used Shortest Path-enclosed Tree (SPT) to include necessary context information outside SPT. Second, it pr oposes a context -sensitive convolution tree kernel, which enumerates both context-free and contextsensitive sub-trees by consid ering their ancestor node paths as their contexts. Moreover, this paper evaluates the complementary nature between our tree kernel and a state -of-the-art linear kernel. Evaluation on the ACE RDC corpora shows that our dynamic context-sensitive tree span is much more suitable for relation extraction than SPT and our tree kernel outperforms the state-of-the-art Collins and Duffy’s convolution tree kernel. It also shows that our tree kernel achieves much better performance than the state-of-the-art linear kernels . Finally, it shows that feature-based and tree kernel-based methods much complement each other and the composite kernel can well integrate both flat and structured features.