Concurrent rebalancing on hyperred-black trees

The HyperRed-Black trees are a relaxed version of Red-Black trees accepting high degree of concurrency. In the Red-Black trees consecutive red nodes are forbidden. This restriction has been withdrawn in the Chromatic trees. They have been introduced by O.~Nurmi and E.~Soisalon-Soininen to work in a concurrent environment. A Chromatic tree can have big clusters of red nodes surrounded by black nodes. Nevertheless, concurrent rebalancing of Chromatic trees into Red-Black trees has a serious drawback: in big cluster of red nodes only the top node can be updated. Direct updating inside the cluster is forbidden. This approach gives us limited degree of concurrency. The HyperRed-Black trees has been designed to solve this problem. It is possible to update red nodes in the inside of a red cluster. In a HyperRed-Black tree nodes can have a multiplicity of colors; they can be red, black or hyper-red.Postprint (published version

Generation, Ranking and Unranking of Ordered Trees with Degree Bounds

We study the problem of generating, ranking and unranking of unlabeled ordered trees whose nodes have maximum degree of $\Delta$. This class of trees represents a generalization of chemical trees. A chemical tree is an unlabeled tree in which no node has degree greater than 4. By allowing up to $\Delta$ children for each node of chemical tree instead of 4, we will have a generalization of chemical trees. Here, we introduce a new encoding over an alphabet of size 4 for representing unlabeled ordered trees with maximum degree of $\Delta$. We use this encoding for generating these trees in A-order with constant average time and O(n) worst case time. Due to the given encoding, with a precomputation of size and time O(n^2) (assuming $\Delta$ is constant), both ranking and unranking algorithms are also designed taking O(n) and O(nlogn) time complexities.Comment: In Proceedings DCM 2015, arXiv:1603.0053

Embedding complete ternary tree in hypercubes using AVL trees

A complete ternary tree is a tree in which every non-leaf vertex has exactly three children. We prove that a complete ternary tree of height h, TTh, is embeddable in a hypercube of dimension . This result coincides with the result of [2]. However, in this paper, the embedding utilizes the knowledge of AVL trees. We prove that a subclass of AVL trees is a subgraph of hypercube. The problem of embedding AVL trees in hypercube is an independent emerging problem

Space saving generalization of B-trees with 23 utilization

AbstractThe paper studies balanced trees with variable length records. It generalizes the concept of B-tree with unfixed key length introduced in [1] and S(1)-tree of [2]. The main property of the new trees, called S(b)-trees, is their local incompressibility. That is, any sequence consisting of b + 1 neighboring nodes of the tree cannot be compressed into a b well formed node. The case of S(2)-trees is studied in detail. For these trees, 23 − ε utilization lower bound is proven, where ε is inversely proportional to the tree branching. Logarithmic running time algorithms for search, insertion, and deletion are presented

An Empirical study on Predicting Blood Pressure using Classification and Regression Trees

Blood pressure diseases have become one of the major threats to human health. Continuous measurement of bloodpressure has proven to be a prerequisite for effective incident prevention. In contrast with the traditional prediction models with lowmeasurement accuracy or long training time, non-invasive blood pressure measurement is a promising use for continuousmeasurement. Thus in this paper, classification and regression trees (CART) are proposed and applied to tackle the problem. Firstly,according to the characteristics of different information, different CART models are constructed. Secondly, in order to avoid theover-fitting problem of these models, the cross-validation method is used for selecting the optimum parameters so as to achieve thebest generalization of these models. Based on the biological data collected from CM400 monitor, this approach has achieved betterperformance than the common existing models such as linear regression, ridge regression, the support vector machine and neuralnetwork in terms of accuracy rate, root mean square error, deviation rate, Theil IC, and the required training time is also comparativelyless. With increasing data, the accuracy rate of predicting systolic blood pressure and diastolic blood pressure by CART exceeds 90%,and the training time is less than 0.5s

On non-recursive trade-offs between finite-turn pushdown automata

It is shown that between one-turn pushdown automata (1-turn PDAs) and deterministic finite automata (DFAs) there will be savings concerning the size of description not bounded by any recursive function, so-called non-recursive tradeoffs. Considering the number of turns of the stack height as a consumable resource of PDAs, we can show the existence of non-recursive trade-offs between PDAs performing k+ 1 turns and k turns for k >= 1. Furthermore, non-recursive trade-offs are shown between arbitrary PDAs and PDAs which perform only a finite number of turns. Finally, several decidability questions are shown to be undecidable and not semidecidable