Solving the Maximum Agreement Subtree and Maximum Compatible Tree Problems on Many Bounded Degree Trees

Abstract : Given a set of leaf-labeled trees with identical leaf sets, the well-known MAXIMUM AGREEMENT SUBTREE (MAST) consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. Its variant called MAXIMUM COMPATIBLE TREE (MCT) is less stringent, as it allows the input trees to be refined. Both problems are of particular interest in computational biology, where trees encountered have often small degrees. In this paper, we study the parameterized complexity of MAST and MCT with respect to the maximum degree, denoted D, of the input trees. While MAST is polynomial for bounded D, we show that MAST is W[1]-hard with respect to parameter D. Moreover, relying on recent advances in parameterized complexity we obtain a tight lower bound: while MAST can be solved in O(N^{O(D)}) time where N denotes the input length, we show that an O(N^{o(D)}) bound is not achievable, unlesss SNP is included in SE. We also show that MCT is W[1]-hard with respect to D, and that MCT cannot be solved in O(n^{o(2^{D/2})}) time, unless SNP is included in SE.
Type de document :
Communication dans un congrès
Moshe Lewenstein; Gabriel Valiente. CPM: Combinatorial Pattern Matching, Jul 2006, Barcelona, Spain. Springer, 17th Annual Symposium on Combinatorial Pattern Matching, LNCS (4009), pp.165-176, 2006, 〈http://www.lirmm.fr/mab〉. 〈10.1007/11780441_16〉
Liste complète des métadonnées

https://hal-lirmm.ccsd.cnrs.fr/lirmm-00145453
Contributeur : Sylvain Guillemot <>
Soumis le : jeudi 10 mai 2007 - 13:29:40
Dernière modification le : jeudi 24 mai 2018 - 15:59:22

Lien texte intégral

Identifiants

Collections

Citation

Sylvain Guillemot, François Nicolas. Solving the Maximum Agreement Subtree and Maximum Compatible Tree Problems on Many Bounded Degree Trees. Moshe Lewenstein; Gabriel Valiente. CPM: Combinatorial Pattern Matching, Jul 2006, Barcelona, Spain. Springer, 17th Annual Symposium on Combinatorial Pattern Matching, LNCS (4009), pp.165-176, 2006, 〈http://www.lirmm.fr/mab〉. 〈10.1007/11780441_16〉. 〈lirmm-00145453〉

Partager

Métriques

Consultations de la notice

72