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Agreement forest : ウィキペディア英語版 | Agreement forest
In the mathematical field of graph theory, an agreement forest for two given (leaf-labeled, irreductible) trees is any (leaf-labeled, irreductible) forest which can, informally speaking, be obtained from both trees by removing a common number of edges. Agreement forests first arose when studying combinatorial problems related to computational phylogenetics, in particular tree rearrangements. == Preliminaries ==
Recall that a tree (or a forest) is irreductible when it lacks any internal node of degree 2. In the case of a rooted tree (or a rooted forest), the root(s) are of course allowed to have degree 2, since they are not internal nodes. Any tree (or forest) can be made irreductible by applying a sequence of edge contractions. An irreductible (rooted or unrooted) tree whose leaves are bijectively labeled by elements of a set is called a (rooted or unrooted) -tree. Such a -tree usually model a phylogenetic tree, where the elements of (the taxon set) could represent species, individual organisms, DNA sequences, or other biological objects. Two -trees and are said to be isomorphic when there exists a graph isomorphism between them which preserves the leaf labels. In the case of rooted -trees, the isomorphism must also preserves the root. Given a -tree and a taxon subset , the minimal subtree of that connects all leaves in is denoted by . When is rooted, then is also rooted, with its root being the node closest to the original root of . This subtree needs not be a -tree, because it might not be irreductible. We therefore further define the restricted subtree , which is obtained from by suppressing all internal nodes of degree 2, yielding a proper -tree.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Agreement forest」の詳細全文を読む
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