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Maximum agreement and compatible supertrees
 Proceedings of the 15th Combinatorial Pattern Matching Symposium (CPM’O4), volume 3109 of LNCS
, 2004
"... Given a set of leaflabelled trees with identical leaf sets, the MAST problem, respectively MCT problem, consists of finding a largest subset of leaves such that all input trees restricted to these leaves are isomorphic, respectively compatible. In this paper, we propose extensions of these problem ..."
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Cited by 20 (8 self)
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Given a set of leaflabelled trees with identical leaf sets, the MAST problem, respectively MCT problem, consists of finding a largest subset of leaves such that all input trees restricted to these leaves are isomorphic, respectively compatible. In this paper, we propose extensions of these problems to the context of supertree inference, where input trees have nonidentical leaf sets. This situation is of particular interest in phylogenetics. The resulting problems are called SMAST and SMCT. A sufficient condition is given that identifies cases where these problems can be solved by resorting to MAST and MCT as subproblems. This condition is met, for instance, when only two input trees are considered. Then we give algorithms for SMAST and SMCT that benefit from the link with the subtree problems. These algorithms run in time linear to the time needed to solve MAST, respectively MCT, on an instance of the same or smaller size. It is shown that arbitrary instances of SMAST and SMCT can be turned in polynomial time into instances composed of trees with a bounded number of leaves. SMAST is shown to be W[2]hard when the considered parameter is the number of input leaves that have to be removed to obtain the agreement of the input trees. A simlar result holds for SMCT. Moreover, the corresponding optimization problems, that is the complements of SMAST and SMCT, can not be approximated in polynomial time within a constant factor, unless P = NP. These results also hold when the input trees have a bounded number of leaves. The presented results apply to both collections of rooted and unrooted trees. Preprint submitted to Elsevier Science 17 November 2006 1
Improved Parameterized Complexity of the Maximum Agreement Subtree and . . .
 IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS
, 2006
"... Given a set of evolutionary trees on a same set of taxa, the maximum agreement subtree problem (MAST), respectively maximum compatible tree problem (MCT), consists of finding a largest subset of taxa such that all input trees restricted to these taxa are isomorphic, respectively compatible. These ..."
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Cited by 9 (4 self)
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Given a set of evolutionary trees on a same set of taxa, the maximum agreement subtree problem (MAST), respectively maximum compatible tree problem (MCT), consists of finding a largest subset of taxa such that all input trees restricted to these taxa are isomorphic, respectively compatible. These problems
PhySIC: A Veto Supertree Method with Desirable Properties
, 2007
"... This paper focuses on veto supertree methods; i.e., methods that aim at producing a conservative synthesis of the relationships agreed upon by all source trees. We propose desirable properties that a supertree should satisfy in this framework, namely the noncontradiction property (PC) and the indu ..."
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Cited by 9 (2 self)
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This paper focuses on veto supertree methods; i.e., methods that aim at producing a conservative synthesis of the relationships agreed upon by all source trees. We propose desirable properties that a supertree should satisfy in this framework, namely the noncontradiction property (PC) and the induction property (PI). The former requires that the supertree does not contain relationships that contradict one or a combination of the source topologies, whereas the latter requires that all topological information contained in the supertree is present in a source tree or collectively induced by several source trees. We provide simple examples to illustrate their relevance and that allow a comparison with previously advocated properties. We show that these properties can be checked in polynomial time for any given rooted supertree. Moreover, we introduce the PhySIC method (PHYlogenetic Signal with induction and nonContradiction). For k input trees spanning a set of n taxa, this method produces a supertree that satisfies the abovementioned properties in O(kn3 + »4) computing time. The polytomies of the produced supertree are also tagged by labels indicating areas of conflict as well as those with insufficient overlap. As a whole, PhySIC enables the user to quickly summarize consensual information of a set of trees and localize groups of taxa for which the data require consolidation. Lastly, we illustrate the behaviour of PhySIC on primate data sets of various sizes, and propose a supertree covering 95 % of all primate extant genera. The PhySIC algorithm is available at http://atgc.lirmm.fr/cgibin/PhySIC.
Approximating the spanning star forest problem and its applications to genomic sequence alignment
 In SODA
, 2007
"... Abstract. This paper studies the algorithmic issues of the spanning star forest problem. We prove the following results: (1) There is a polynomialtime approximation scheme for planar graphs; (2) there is a polynomialtime 3approximation algorithm for graphs; (3) it is NPhard to approxi5 mate the ..."
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Cited by 8 (2 self)
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Abstract. This paper studies the algorithmic issues of the spanning star forest problem. We prove the following results: (1) There is a polynomialtime approximation scheme for planar graphs; (2) there is a polynomialtime 3approximation algorithm for graphs; (3) it is NPhard to approxi5 mate the problem within ratio 259 + ɛ for graphs; (4) there is a lineartime algorithm to compute the 260 maximum star forest of a weighted tree; (5) there is a polynomialtime 1approximation algorithm 2 for weighted graphs. We also show how to apply this spanning star forest model to aligning multiple genomic sequences over a tandem duplication region. Key words. Dominating set, spanning star forest, approximation algorithm, genomic sequence alignment AMS subject classifications. 68Q17, 68Q25, 68R10, 68W25 1. Introduction. A
Improved approximation algorithms for the spanning star forest problem
 Proc. APPROX 2007, LNCS
"... Abstract. A star graph is a tree of diameter at most two. A star forest is a graph that consists of nodedisjoint star graphs. In the spanning star forest problem, given an unweighted graph G, the objective is to find a star forest that contains all the vertices of G and has the maximum number of ed ..."
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Cited by 7 (1 self)
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Abstract. A star graph is a tree of diameter at most two. A star forest is a graph that consists of nodedisjoint star graphs. In the spanning star forest problem, given an unweighted graph G, the objective is to find a star forest that contains all the vertices of G and has the maximum number of edges. This problem is the complement of the dominating set problem in the following sense: On a graph with n vertices, the size of the maximum spanning star forest is equal to n minus the size of the minimum dominating set. We present a 0.71approximation algorithm for this problem, improving upon the approximation factor of 0.6 of Nguyen et al. [9]. We also present a 0.64approximation algorithm for the problem on nodeweighted graphs. Finally, we present improved hardness of approximation results for the weighted versions of the problem. 1
Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2007).
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Consensus of Trees.
, 2008
"... This problem is a pattern matching problem on leaflabeled trees. Each input tree is considered as a branching pattern inducing specific groups of leaves. Given a set of input trees with identical leaf sets, the goal is to find a largest subset of leaves on the branching pattern of which the input t ..."
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This problem is a pattern matching problem on leaflabeled trees. Each input tree is considered as a branching pattern inducing specific groups of leaves. Given a set of input trees with identical leaf sets, the goal is to find a largest subset of leaves on the branching pattern of which the input trees do not disagree. A maximum compatible tree is a tree with such a leafset and with the branching patterns associated to these leaves by the input trees. The Maximum Compatible Tree problem (mct) is to find such a tree or, equivalently, its leaf set. The main motivation for this problem is in phylogenetics, to measure the similarity between evolutionary trees, or to represent a consensus of a set of trees. The problem was introduced in [9] and [10, under the MRST acronym]. Previous related works concern the wellknown Maximum Agreement Subtree problem (mast). Solving mast is finding a largest subset of leaves on which all input trees exactly agree. The difference between mast and mct, is that mast seeks a tree whose branching information is isomorphic to that of a subtree in each of the input trees, while mct seeks a tree that contains the branching information (i.e. groups) of a subtree of each input tree. This difference allows the tree obtained for mct to be more informative, as it can include branching information present in one input tree but not in the others, as long as this information is compatible with them. Both problems are equivalent when
SYNONYMS: maximum refinement subtree (MRST).
"... This problem is a pattern matching problem on leaflabeled trees. Each input tree is considered as a branching pattern inducing specific groups of leaves. Given a set of input trees with identical leaf sets, the goal is to find a largest subset of leaves on the branching pattern of which the input t ..."
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This problem is a pattern matching problem on leaflabeled trees. Each input tree is considered as a branching pattern inducing specific groups of leaves. Given a set of input trees with identical leaf sets, the goal is to find a largest subset of leaves on the branching pattern of which the input trees do not disagree. A maximum compatible tree is a tree with such a leafset and with the branching patterns associated to these leaves by the input trees. The Maximum Compatible Tree problem (mct) is to find such a tree or, equivalently, its leaf set. The main motivation for this problem is in phylogenetics, to measure the similarity between evolutionary trees, or to represent a consensus of a set of trees. The problem was introduced in [9] and [10, under the MRST acronym]. Previous related works concern the wellknown Maximum Agreement Subtree problem (mast). Solving mast is finding a largest subset of leaves on which all input trees exactly agree. The difference between mast and mct, is that mast seeks a tree whose branching information is isomorphic to that of a subtree in each of the input trees, while mct seeks a tree that contains the branching information (i.e. groups) of a subtree of each input tree. This difference allows the tree obtained for mct to be more informative, as it can include branching information present in one input tree but not in the others, as long as this information is compatible with them. Both problems are equivalent when