Search results for "Weight-balanced tree"
showing 10 items of 10 documents
The Myriad Virtues of Wavelet Trees
2009
Wavelet Trees have been introduced in [Grossi, Gupta and Vitter, SODA '03] and have been rapidly recognized as a very flexible tool for the design of compressed full-text indexes and data compressors. Although several papers have investigated the beauty and usefulness of this data structure in the full-text indexing scenario, its impact on data compression has not been fully explored. In this paper we provide a complete theoretical analysis of a wide class of compression algorithms based on Wavelet Trees. We also show how to improve their asymptotic performance by introducing a novel framework, called Generalized Wavelet Trees, that aims for the best combination of binary compressors (like,…
Alternating model trees
2015
Model tree induction is a popular method for tackling regression problems requiring interpretable models. Model trees are decision trees with multiple linear regression models at the leaf nodes. In this paper, we propose a method for growing alternating model trees, a form of option tree for regression problems. The motivation is that alternating decision trees achieve high accuracy in classification problems because they represent an ensemble classifier as a single tree structure. As in alternating decision trees for classification, our alternating model trees for regression contain splitter and prediction nodes, but we use simple linear regression functions as opposed to constant predicto…
Ranking and unrankingk-ary trees with a 4k –4 letter alphabet
1997
Abstract The problem of the direct generation in A-order of binary trees was stated by Zaks in 1980. In 1988 Roelants van Baronaigien and Ruskey gave a solution for k-ary trees with n internal nodes using an encoding sequence of kn+1 integers between 1 and n. Vajnovszki and Pallo improved this result for binary trees in 1994 using words of length n–1 on a four letter alphabet. Recently Korsh generalized the Vajnovszki and Pallo’s generating algorithm to k-ary trees using an alphabet whose cardinality depends on k but not on n. We give in this paper ranking and unranking algorithms for k-ary trees using the Korsh’s encoding scheme.
Nearly tight bounds on the learnability of evolution
2002
Evolution is often modeled as a stochastic process which modifies DNA. One of the most popular and successful such processes are the Cavender-Farris (CF) trees, which are represented as edge weighted trees. The Phylogeny Construction Problem is that of, given /spl kappa/ samples drawn from a CF tree, output a CF tree which is close to the original. Each CF tree naturally defines a random variable, and the gold standard for reconstructing such trees is the maximum likelihood estimator of this variable. This approach is notoriously computationally expensive. We show that a very simple algorithm, which is a variant on one of the most popular algorithms used by practitioners, converges on the t…
On the listing and random generation of hybrid binary trees
1994
We consider in this paper binary trees whose internal nodes are either associative or non-associative. Hybrid binary trees are equivalence classes with respect to the associative property. We count, list and generate randomly hybrid binary trees using Fibonacci numbers.
Generation of Valid Labeled Binary Trees
2003
International audience; Generating binary trees is a well-known problem. In this paper, we add some constraints to leaves of these trees. Such trees are used in the morphing of polygons, where a polygon P is represented by a binary tree T and each angle of P is a weight on a leaf of T. In the following, we give two algorithms to generate all binary trees, without repetitions, having the same weight distribution to their leaves and representing all parallel polygons to P.
The Rotation χ-Lattice of Ternary Trees
2001
This paper generalizes to k-ary trees the well-known rotation transformation on binary trees. For brevity, only the ternary case is developped. The rotation on ternary trees is characterized using some codings of trees. Although the corresponding poset is not a lattice, we show that it is a χ-lattice in the sense of Leutola–Nieminen. Efficient algorithms are exhibited to compute meets and joins choosen in a particular way.
Almost disjoint spanning trees: relaxing the conditions for completely independent spanning trees
2017
International audience; The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these notions by dening (i, j)-disjoint spanning trees, where i (j, respectively) is the number of vertices (edges, respectively) that are shared by more than one tree. We illustrate how (i, j)-disjoint spanning trees provide some nuances between the existence of disjoint connected dominating sets and completely independent spanning trees. We prove that determining if there exist two (i, j)-disjoint spanning trees in a graph G is NP-comple…
SYSTOLIC GENERATION OF k-ARY TREES
1999
The only parallel generating algorithms for k-ary trees are those of Akl and Stojmenović in 1996 and of Vajnovszki and Phillips in 1997. In the first of them, trees are represented by an inversion table and the processor model is a linear aray multicomputer. In the second, trees are represented by bitstrings and the algorithm executes on a shared memory multiprocessor. In this paper we give a parallel generating algorithm for k-ary trees represented by generalized P–sequences for execution on a linear array multicomputer.
Right-arm rotation distance between binary trees
2003
We consider a transformation on binary trees, named right-arm rotation, which is a special instance of the well-known rotation transformation. Only rotations at nodes of the right arm of the trees are allowed. Using ordinal tools, we give an efficient algorithm for computing the right-arm rotation distance between two binary trees, i.e., the minimum number of rightarm rotations necessary to transform one tree into the other.