X-tree Research Articles

Sur le plus grand sous-arbre commun à plusieurs X-arbres

Étant donnés plusieursX-arbres, ou arbres phylogénétiques, sur le même ensembleX, nous cherchons à construire un plus grand sous-ensembleY⊂Xtel que les arbres partiels induits surYsoient identiques d’un point de vue topologique, c’est-à-dire indépendamment des longueurs des arêtes. Ce problème, connu sous le nom de MAST (Maximum Agreement SubTree), est NP-Difficile, dans le cas général, dès que le nombre deX-arbres est supérieur à 2. Nous présentons un algorithme approché qui construit un arbre partiel commun maximal. Il est facilement programmable et suffisamment efficace sur une centaine deX-arbres connectant une centaine d’éléments pour évaluer la taille moyenne d’un sous-arbre commun à desX-arbres indépendants. La distribution observée permet d’estimer la taille critique d’un sous-arbre commun et de mesurer la congruence de plusieurs arbres évolutifs.

Two-centre tree topologies for metropolitan area networks

A two-centre binary tree (BT) can be constructed by linking the root nodes of two binary trees. Variations can also be constructed by making additional linkages within the two-centre binary tree. Three of these variations, referred to as the quaternary tree (QT), the X-tree (XT) and the ring tree (RT), are studied. Comparisons using performance measures of traffic flows and path reliabilities are made with respect to the BT and some popular topologies in the literature. Various implementations issues that take advantage of these tree networks are then proposed and discussed. The study indicates that the variants of the two-centre trees are viable topologies for the implementation of a metropolitan area network (MAN).

Terminal-pair reliability of tree-type computer communication networks : Oliver W. W. Yang. IEEE Trans. Reliab.41, 49 (1992)

Analysis is presented for computing the terminal pair reliabilities of the two-centered tree(2CT). the X-tree(XT) and the ring-tree(RT). A building block is identified in the 2CT lrom which a decomposition algorithm is formulated. Another building block is identified for the XT and RT from which a truss-transformation method and a computational algorithm are obtained. By comparison, it is shown that an XT is a good candidate for applications such as high bandwidth networks with high link reliability.