Balance in trees
نویسندگان
چکیده
We show that the set of vertices in a treeT of smallest weight balance is the (branchweight) centroid. We characterize the set of edges in T with smallest weight-edge difference in terms of the vertices of smallest weight balance. A similar characterization is obtained for the set of edges in T with smallest distance-edge difference in terms of the vertices of smallest distance balance. This yields a new proof that the set of vertices in T of smallest distance balance consists of a single vertex or two adjacent vertices (possibly disjoint from the center and the branch weight centroid). © 2005 Elsevier B.V. All rights reserved.
منابع مشابه
Limit distribution of the quartet balance index for Aldous's b>=0-model
This note accompanies T. Mart́ınez–Coronado, A. Mir, F. Rosselló and G. Valiente’s work “A balance index for phylogenetic trees based on quartets”, introducing a new balance index for trees. We show here that this balance index, in the case of Aldous’s β ≥ 0–model, convergences weakly to a contraction–type distribution.
متن کاملComplexity of Layered Binary Search Trees with Relaxed Balance
When search trees are made relaxed, balance constraints are weakened such that updates can be made without immediate rebalancing. This can lead to a speed-up in some circumstances. However, the weakened balance constraints also make it more challenging to prove complexity results for relaxed structures. In our opinion, one of the simplest and most intuitive presentations of balanced search tree...
متن کاملAssessing the capacity of trees and shrubs species to accumulate of particulate matter (PM10, PM2.5 and PM0.2)
Background and Objective: Today, the presence and increase of particulate matter is one of the serious factors that threaten human health. In the meantime, trees can accumulate airborne particles by their foliage. In this study, the accumulating ability of various PM by the leaf of some tree and shrub species was evaluated in Isfahan. Materials and Methods: 12 species of trees and shrubs were ...
متن کاملOn Balance Index Sets of Rooted Trees
Any vertex labeling f : V → {0, 1} of the graph G = (V, E) induces a partial edge labeling f∗ : E → {0, 1} defined by f∗(uv) = f(u) if and only if f(u) = f(v). The balance index set of G is defined as {|f∗−1(0) − f∗−1(1)| : |f−1(0) − f−1(1)| ≤ 1}. In this paper, we first determine the balance index sets of rooted trees of height not exceeding two, thereby completely settling the problem for tre...
متن کاملExtremal values of the Sackin balance index for rooted binary trees
Tree balance plays an important role in different research areas like theoretical computer science and mathematical phylogenetics. For example, it has long been known that under the Yule model, a pure birth process, imbalanced trees are more likely than balanced ones. Therefore, different methods to measure the balance of trees were introduced. The Sackin index is one of the most frequently use...
متن کاملA balance index for phylogenetic trees based on quartets
We define a new balance index for phylogenetic trees based on the symmetry of the evolutive history of every quartet of leaves. This index makes sense for polytomic trees and it can be computed in time linear in the number of leaves. We compute its maximum and minimum values for arbitrary and bifurcating trees, and we provide exact formulas for its expected value and variance for bifurcating tr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 304 شماره
صفحات -
تاریخ انتشار 2005