Binary search trees are a fundamental data structure and their height plays a key role in the analysis of divide-and-conquer algorithms like quicksort. Their worst-case height is linear; their average height, whose exact value is one of the best-studied problems in average-case complexity, is logarithmic. We analyze their smoothed height under additive noise: An adversary chooses a sequence of ...

T O D O :U pate gant nfo Abstract. An (n, d)-expander is a graph G = (V,E) such that for every X ⊆ V with |X| ≤ 2n − 2 we have |ΓG(X)| ≥ (d+1)|X|. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any (n, d)-expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for o...

fire, as a natural ecological disturbance factor in forest, this study located in the marivan region, northern zagros forest, and western iranian state of kurdistan. in each burned and unburned area 30 circle sample plot (1000 m2) were collected by randomized–systematic method in the 100×200 m net (in total 60 plots). in every sample plot the kind of species, number of tree, the height of coppi...

The probability that a random walker returns to its origin for large times scales as t;{-d[over ]2} , where d[over ] is the spectral dimension. We calculate d[over ] for a class of tree structures using a renormalization technique on an infinite continued fraction. We consider a wide range of homogeneous networks based on replacing the branches of a self-similar tree with arbitrary fractals and...

In this paper, we study data structures for use in N-body simulation. We concentrate on the spatial decomposition tree used in particle-cluster force evaluation algorithms such as the Barnes-Hut algorithm. We prove that a k-d tree is asymptot-ically inferior to a spatially balanced tree. We show that the worst case complexity of the force evaluation algorithm using a k-d tree is (n log 3 n log ...

The elimination tree is a rooted tree that is computed from the adjacency graph of a symmetric matrix A. The height of the elimination tree is one restricting factor when solving a sparse linear system Ax = b on a parallel computer using Cholesky factorization. An eecient algorithm is presented for the problem of ordering the nodes in a tree G so that its elimination tree is of minimum height. ...

Given a set S of n points on d, we show, for fixed d, how to construct in Ž . Ž . O n log n time a data structure we call the balanced aspect ratio BAR tree. A Ž . BAR tree is a binary space partition tree on S that has O log n depth in which Ž . every region is convex and ‘‘fat’’ that is, has a bounded aspect ratio . While previous hierarchical data structures such as k-d trees, quadtrees, oct...