On the Approximation of Computing Evolutionary Trees

Berry, Vincent; Guillemot, Sylvain; Nicolas, François; Paul, Christophe

doi:10.1007/11533719_14

Cited by 19 publications

(24 citation statements)

References 26 publications

(41 reference statements)

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“…The complement of MAST, respectively MCT, is defined to be the restriction of CSMAST, respectively CSMCT, to instances consisting in collections of trees sharing the same leaf set. The complement of MCT is approximable within ratio 3 [19], as is also well-known for the complement of MAST ( [2,7]). …”

Section: Reduction To Instances Involving Smaller Treesmentioning

confidence: 57%

“…The MAST problem (maximizing the number of leaves in an agreement subtree) is hard to approximate on a bounded number of trees [27] or on trees with a bounded height [21]. The same results hold for MCT [7].…”

Section: Related Workmentioning

confidence: 86%

“…minimizing the number of leaves to remove so that input trees are isomorphic) can be approximated within a constant ratio in polynomial time in both rooted and unrooted cases 7 [2,7,28]. The same result holds for the complement problem of MCT [19,7].…”

Section: Related Workmentioning

confidence: 94%

“…In the same way, building on a result of [7], approximating SMCT on rooted triples is at least as hard as approximating Maximum Independent Set. The complement of MAST, respectively MCT, is defined to be the restriction of CSMAST, respectively CSMCT, to instances consisting in collections of trees sharing the same leaf set.…”

Section: Reduction To Instances Involving Smaller Treesmentioning

confidence: 96%

“…The Maximum Compatible Tree problem (MCT) is a variant of MAST that takes this into account by seeking a largest set of leaves such that the source trees restricted to these leaves are compatible [25,27,20,7] (note that this problem is also called MRST in [27]). Compatibility allows a high-degree node of a source tree to be resolved (split into several nodes) according to the information present in other source trees.…”

Section: Introductionmentioning

confidence: 99%

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Maximum Agreement and Compatible Supertrees

Berry

Nicolas

2004

Lecture Notes in Computer Science

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Given a set of leaf-labelled 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 non-identical 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.

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Section: Reduction To Instances Involving Smaller Treesmentioning

confidence: 57%