A. Amir and D. Keselman, "Maximum agreement subtree in a set of evolutionary trees: metrics and e#cient algorithm," SIAM Journal on Computing, vol. 26, no. 6, pp. 1656--1669, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of species X , and a positive integer k. Question: Is there a subset S X of size at most k such that T i restricted to the leaf set X = X Gamma S is the same (up to label preserving isomorphism and ignoring vertices of degree 2) for i = 1; r All of these problems are NP complete ([GJ79, AK94]) and are described above in the standard way for the parameterized complexity framework. Part of the input (which may be some aggregate of various aspects of the input) is identified as the parameter for the problem specification. In order to consider a parameterized problem classically, just ....

A. Amir and D. Keselman, "Maximum Agreement Subtree in a Set of Evolutionary Trees -- Metrics and Efficient Algorithms," In: 35th Annual Symposium on Foundations of Computer Science, 758--769, 1994.

....takes O(n log n) time. This algorithm takes O(min nd log d log n, nd log n ) for degree d trees. Finally, Cole and Hariharan [CR96] improved the algorithm from [FPT95a] to an O(n log n) algorithm. The MAST problem for more than two trees has also been studied. Amir and Keselman [AK97] showed that the problem is NP hard for even 3 unbounded degree trees. However, polynomial bounds are known [AK97, FPT95b] for three or more bounded degree trees. Our Contribution. This paper is the combined journal version of [FPT95a] and [CR96] and presents an O(n log n) algorithm for the MAST ....

....Finally, Cole and Hariharan [CR96] improved the algorithm from [FPT95a] to an O(n log n) algorithm. The MAST problem for more than two trees has also been studied. Amir and Keselman [AK97] showed that the problem is NP hard for even 3 unbounded degree trees. However, polynomial bounds are known [AK97, FPT95b] for three or more bounded degree trees. Our Contribution. This paper is the combined journal version of [FPT95a] and [CR96] and presents an O(n log n) algorithm for the MAST problem for two binary trees. The O(n log n) algorithm of [FPT95a] can be viewed as taking the following approach ....

A. Amir, D. Keselman. Maximum agreement subtree in a set of evolutionary trees. SIAM Journal on Computing, 26(6), pp. 1656-1669, 1997.

....is a basic approach that allows to reconciliate di erent evolutionary trees over the same set of species: it computes a subset of the extant species about which all trees agree . A general way to de ne an agreement subtree from a set T 1 ; T k of S labeled trees has been formalized in [1]. This method assumes that each edge is labeled by an interval weight (a range of time to measure the duration of the evolution process) and looks for a subset S of the extant species S such that: each edge of the subtree induced in each tree of the given set is labeled by a value belonging ....

....Sung and Ting [25] which described a technique allowing to match the time complexity of the two previously cited algorithms also in the case of unrooted trees. The problems MHT and MIT over a set of trees, where at least one of the trees has bounded degree, can be solved in polynomial time [1], even though the time complexity is exponential in the bound for the degree. Moreover both problems are NP hard for instances containing three trees of unbounded degree, hence it is necessary to focus on designing polynomial time approximation algorithms. The approximation complexity of the MHT ....

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A. Amir and D. Keselman. Maximum agreement subtree in a set of evolutionary trees: Metrics and ecient algorithms. SIAM Journal on Computing, 26(6):1656{ 1669, 1997.

....two evolutionary trees is to determine a consensus tree (or forest) that reflects common traits of the two trees, e.g. the maximum agreement subtree. Much work has been concerned with developing e#cient methods for computing the maximum agreement subtree of two or more evolutionary trees, see e.g. [2]. Another approach for comparing two evolutionary trees is to define a distance measure between two trees and compare the two trees by computing the distance. Several distance measures have been proposed, e.g. the symmetric di#erence metric [12] the nearest neighbor interchange metric [16] the ....

A. Amir and D. Keselman. Maximum agreement subtree in a set of evolutionary trees: Metrics and e#cient algorithms. SIAM Journal on Computing, 26(6):1656-- 1669, 1997.

....two evolutionary trees is to determine a consensus tree (or forest) that re ects common traits of the two trees, e.g. the maximum agreement subtree. Much work has been concerned with developing ecient methods for computing the maximum agreement subtree of two or more evolutionary trees, see e.g. [2]. Another approach for comparing two evolutionary trees is to de ne a distance measure between two trees and compare the two trees by computing the distance. Several distance measures have been proposed, e.g. the symmetric di erence metric [12] the nearest neighbor interchange metric [16] the ....

A. Amir and D. Keselman. Maximum agreement subtree in a set of evolutionary trees: Metrics and ecient algorithms. SIAM Journal on Computing, 26(6):1656-1669, 1997.

....agreement subtree (MAST) problem for three trees with unbounded degree cannot be approximated within ratio 2 log n in polynomial time for any 1, unless NP DTIME[2 polylog n ] and MAST with edge contractions for two binary trees is NP hard. This answers two open questions posed in [1]. For the maximum re nement subtree (MRST) problem involving two trees, we show that it is polynomial time solvable when both trees have bounded degree and is NP hard when one of the trees can have an arbitrary degree. Finally, we consider the problem of optimally transforming a tree into another ....

....set of the disagreed species. A maximum agreement subtree (MAST) of T 1 and T 2 is an AST with the largest number of leaves (i.e. the largest number of species have been agreed upon) The notion of AST and MAST can be easily extended to more than two evolutionary trees on the same set of species [1]. The rst polynomial time algorithm for MAST on two trees was given by Steel and Warnow [17] Their algorithm runs in O(n 2 ) time for bounded degree trees and O(n 4:5 log n) for unboundeddegree trees, where n is number of species. Farach and Thorup recently improved the running time to O(n ....

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A. Amir and D. Keselman, Maximum agreement subtree in a set of evolutionary trees - metrics and ecient algorithms, Proc. 35th IEEE Symp. Found. Comp. Sci., 1994.

....of eciently merging and updating such partial subtrees and apply them to the ecient construction and maintenance of evolutionary trees in the experiment model. The problem of constructing evolutionary trees is basic in computational biology. It has been studied extensively in several papers [1, 2, 3, 4, 5, 6, 7]. An evolutionary tree is a tree where the leaves represent species and internal nodes represent their common ancestors, see Fig. 1. There are many di erent approaches to the problem of constructing an evolutionary tree re ecting, among other things, di erent kinds of available data. A well known ....

A. Amir and D. Keselman. Maximum agreement subtree in a set of evolutionary trees: Metrics and ecient algorithms. SIAM Journal on Computing, 26:1656-1669, 1997.

....tree problem. 1 Introduction An evolutionary tree models how different species in a given set have evolved. The leaves in an evolutionary tree correspond to species and internal nodes represent the species ancestors. The problem of finding an evolutionary tree has been studied a lot recently [3, 4, 5, 8, 12, 14, 15, 17, 18]. There are many different approaches, depending on among other things what kind of data that is available. Therefore, various versions of this problem arise in, for example, computational biology when one wants to find out how different species are related, and comparative linguistics, where it ....

....1 Given a set of evolutionary trees dealing with a fixed set of species, one might want to identify a subtree contained within every given tree such that the number of leaves labeled by species is maximized. This problem is known as the maximum homeomorphic agreement subtree problem (MHT) [14]. More formally, it is defined as follows. Given k rooted trees T 1 ; T 2 ; T k , each with n leaves labeled distinctly with elements chosen from a set A of cardinality n, find a maximum cardinality subset B of A such that the minimal homeomorphic subtrees of T 1 ; T 2 ; T k (i.e. with ....

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D. Keselman and A. Amir. Maximum agreement subtree in a set of evolutionary trees - Metrics and efficient algorithms. Proc. of the 35th Annual Symposium on the Foundations of Computer Science (FOCS), 1994, pp. 758-769.

....homeomorphic to the subtree of T i induced by the leaves of T . See Fig. 2 for an example. c d e f a b e f c a d b a b e f c d c f e b a Fig. 2. Three binary input trees with six species yield a maximum agreement subtree with five species. MAST has been studied in many papers, see for example [3, 5, 6, 10, 11, 13]. Keselman and Amir [11] showed that MAST is NP complete, even for three trees, but on the other hand there are polynomial time algorithms for the two tree case [3, 4] and the case where some of the input trees has maximum degree bounded by a constant [3, 11] Polynomial time algorithms are also ....

....by the leaves of T . See Fig. 2 for an example. c d e f a b e f c a d b a b e f c d c f e b a Fig. 2. Three binary input trees with six species yield a maximum agreement subtree with five species. MAST has been studied in many papers, see for example [3, 5, 6, 10, 11, 13] Keselman and Amir [11] showed that MAST is NP complete, even for three trees, but on the other hand there are polynomial time algorithms for the two tree case [3, 4] and the case where some of the input trees has maximum degree bounded by a constant [3, 11] Polynomial time algorithms are also known for the undirected ....

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D. Keselman and A. Amir. Maximum agreement subtree in a set of evolutionary trees -- metrics and e#cient algorithms. In Proceedings of the 35th Annual IEEE Symposium on the Foundations of Computer Science, pages 758--769, 1994. To appear in SIAM Journal on Computing.

....of eciently merging and updating such partial subtrees and apply them to the ecient construction and maintenance of evolutionary trees in the experiment model. The problem of constructing evolutionary trees is basic in computational biology. It has been studied extensively in several papers [1 7]. An evolutionary tree is a tree where the leaves represent species and internal nodes represent their common ancestors, see Fig. 1. There are many di erent approaches to the problem of constructing an evolutionary tree re ecting, among other things, di erent kinds of available data. A well known ....

A. Amir and D. Keselman. Maximum agreement subtree in a set of evolutionary trees: Metrics and ecient algorithms. SIAM Journal on Computing, 26:1656-1669, 1997.

.... have also been used in such diverse areas as compiler design [27, 1] structured text databases [18, 19] and the theory of natural languages [24, 8] More recently, labeled trees have been used in phylogeny and molecular biology, where many of the underlying structures can be modeled with trees [7, 22, 31, 5, 6, 17]. Due to the large number of application areas, often the same or similar problems are studied under different terminology. Of particular interest are methods for combining or comparing the data associated with a pair of trees, as in the following three classes of problems, which can be viewed as ....

....of the topological embedding problem on trees with distinct leaf labels, also known as the Maximum Agreement Subtree Problem. The problem has the following application: given two evolutionary trees derived using different methods, the 1 largest subtree is a more robust evolutionary tree [7, 22, 31, 5, 6, 17]. Farach and Thorup [6] have an O(n 1:5 log n) algorithm; Keselman and Amir [17] consider the problem when there are more than two input trees. A supertree is of interest in the context of editing, image clustering, genetics, and chemical structure analysis, as it gives a measure of the ....

[Article contains additional citation context not shown here]

D. Keselman and A. Amir, Maximum agreement subtree in a set of evolutionary trees - metrics and efficient algorithms, Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 758-769, 1994.

.... pairs of trees (exact matching, approximate matching, subgraph isomorphism, topological embedding, minor containment) 3, 5, 9, 13, 14] In addition, researchers have measured the similarity between trees by finding the largest common subtree or smallest common supertree under various constraints [1, 4, 7, 8, 10, 12, 19]. In this paper we consider the problem of finding the smallest common supertree under minor containment. Concisely, a graph G is a minor of a graph H if it is possible to map all the vertices in G to mutually disjoint connected subgraphs in H and there exists a bijection, from the edges of G to ....

A. Amir and D. Keselman. Maximum agreement subtree in a set of evolutionary trees: metrics and efficient algorithms. SIAM Journal on Computing, 26(6):1656--1669, December 1997.

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A. Amir and D. Keselman, "Maximum agreement subtree in a set of evolutionary trees: metrics and e#cient algorithm," SIAM Journal on Computing, vol. 26, no. 6, pp. 1656--1669, 1997.

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Amir A. and D. Keselman. Maximum agreement subtree in a set of evolutionary trees: metrics and efficient algorithm. SIAM J. on Comp., 26(3):1656--1669, 1997.

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A. Amir and D. Keselman. Maximum agreement subtree in a set of evolutionary trees: metrics and e#cient algorithm. SIAM Journal on Computing, 26(6):1656-- 1669, 1997.

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A. Amir and D. Keselman, "Maximum agreement subtree in a set of evolutionary trees: metrics and efficient algorithm," SIAM Journal on Computing, vol. 26, no. 6, pp. 1656--1669, 1997.

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A. Amir and D. Keselman, "Maximum agreement subtree in a set of evolutionary trees: metrics and e#cient algorithm," SIAM Journal on Computing, vol. 26, no. 6, pp. 1656--1669, 1997.

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Amir A. and D. Keselman. Maximum agreement subtree in a set of evolutionary trees: metrics and efficient algorithm. SIAM J. on Comp., 26(3):1656--1669, 1997.

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Amir, A. and Keselman, D., Maximum agreement subtree in a set of evolutionary trees: metrics and e#cient algorithms, SIAM J. Comput., 26(6):1656--1669, 1997.

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A. Amir and D. Keselman. Maximum agreement subtree in a set of evolutionary trees - metrics and e#cient algorithms. In 35th Annual Symposium on Foundations of Computer Science, pages 758--769, 1994.

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Dmitry Keselman and Amihood Amir. Maximum agreement subtree in a set of evolutionary trees -- metrics and efficient algorithms. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science (FOCS), pages 758--769, 1994.

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A. Amir and D. Keselman. Maximum agreement subtree in a set of evolutionary trees: Metrics and e#cient algorithms. SIAM Journal on Computing, 26(6):1656--1669, 1997.

No context found.

A. Amir and D. Keselman. Maximum agreement subtree in a set of evolutionary trees: metrics and ecient algorithms. SIAM Journal on Computing, 26(6):1656{ 1669, December 1997.

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D. Keselman and A. Amir. Maximum agreement subtree in a set of evolutionary trees { metrics and ecient algorithms. Proc. of 35th Annual IEEE Symposium on the Foundations of Computer Science (FOCS'94), 1994, pp. 758-769.

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Amir, A. and Keselman, D. Maximum Agreement Subtree of a set of Evolutionary Trees - Metrics and Efficient Algorithms, SIAM J. Computing, 1997, Vol. 26, No. 6, pp. 1656-1669, (preliminary version appeared in FOCS 94).

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