Abstract. A hyperplane search tree is a binary tree used to store a set S of n d-dimensional data points. In a random hyperplane search tree for S, the root represents a hyperplane defined by d data points drawn uniformly at random from S. The remaining data points are split by the hyperplane, and the definition is used recursively on each subset. We assume that the data are points in general p...

Suppose we have n keys, n access probabilities for the keys, and n+1 access probabilities for the gaps between the keys. Let hmin(n) be the minimal height of a binary search tree for n keys. We consider the problem to construct an optimal binary search tree with near minimal height, i.e. with height h ≤ hmin(n) +∆ for some fixed ∆. It is shown, that for any fixed∆ optimal binary search trees wi...

In this technical report we present an analysis of the complexity of a class of algorithms. These algorithms recursively explore a binary tree and need to make two recursive calls for one of the subtrees and only one for the other. We derive the complexity of these algorithms in the worst and in the best case and show the tree structures for which these cases happen. 1 The Problem Let us consid...

Hierarchical clustering (HC) is one of the most frequently used methods in computational biology in the analysis of high-dimensional genomics data. Given a data set, HC outputs a binary tree leaves of which are the data points and internal nodes represent clusters of various sizes. Normally, a fixed-height cut on the HC tree is chosen, and each contiguous branch of data points below that height...

knowing and conducting studies on size characters of trees is essential for assessing the tree volumeand/or other statistical parameters and also forest management. the characteristics of 529 treesincluding diameter at breast height (dbh) and total height were measured in an even-aged fraxinusstand for two periods from 2005 to 2012 in chelir district, a part of experimental kheyrud forest.resul...

Topography affects forest canopy height retrieval based on airborne Light Detection and Ranging (LiDAR) data a lot. This paper proposes a method for correcting deviations caused by topography based on individual tree crown segmentation. The point cloud of an individual tree was extracted according to crown boundaries of isolated individual trees from digital orthophoto maps (DOMs). Normalized c...

Tree growth has been reported to increase in response to recent global climate change in controlled and semi-controlled experiments, but few studies have reported response of tree growth to increased temperature and atmospheric carbon dioxide (CO₂) concentration in natural environments. This study addresses how recent global climate change has affected height growth of trembling aspen (Populus ...

In computer graphics, models describing the fractal branching structure of trees typically exploit the modularity of tree structures. The models are based on local production rules, which are applied iteratively and simultaneously to create a complex branching system. The objective is to generate three-dimensional scenes of often many realisticlooking and non-identical trees. Our goal, instead,...

1. Tree height is a key variable for estimating tree biomass and investigating tree life history, but it is difficult to measure in forests with tall, dense canopies and wide crowns. The traditional method, which we refer to as the ‘tangent method’, involves measuring horizontal distance to the tree and angles from horizontal to the top and base of the tree, while standing at a distance of perh...