A tight upper bound for the path length of AVL trees

AbstractWe prove that the internal path length of an AVL tree of size N is bounded from above by 1.4404N(log2 N-log2log2N)+O(N) and show that this bound is achieved by an infinite family of AVL trees, each tree of which is not of maximal height. These results carry over to the comparison cost of brother trees

Search Tree Data Structures and Their Applications

This study concerns the discussion of search tree data structures and their applications. The thesis presents three new top-down updating algorithms for the concurrent data processing environment.Computing and Information Scienc

New Combinatorial Properties and Algorithms for AVL Trees

In this thesis, new properties of AVL trees and a new partitioning of binary search trees named core partitioning scheme are discussed, this scheme is applied to three binary search trees namely AVL trees, weight-balanced trees, and plain binary search trees. We introduce the core partitioning scheme, which maintains a balanced search tree as a dynamic collection of complete balanced binary trees called cores. Using this technique we achieve the same theoretical efficiency of modern cache-oblivious data structures by using classic data structures such as weight-balanced trees or height balanced trees (e.g. AVL trees). We preserve the original topology and algorithms of the given balanced search tree using a simple post-processing with guaranteed performance to completely rebuild the changed cores (possibly all of them) after each update. Using our core partitioning scheme, we simultaneously achieve good memory allocation, space-efficient representation, and cache-obliviousness. We also apply this scheme to arbitrary binary search trees which can be unbalanced and we produce a new data structure, called Cache-Oblivious General Balanced Tree (COG-tree). Using our scheme, searching a key requires O(log_B n) block transfers and O(log n) comparisons in the external-memory and in the cache-oblivious model. These complexities are theoretically efficient. Interestingly, the core partition for weight-balanced trees and COG-tree can be maintained with amortized O(log_B n) block transfers per update, whereas maintaining the core partition for AVL trees requires more than a poly-logarithmic amortized cost. Studying the properties of these trees also lead us to some other new properties of AVL trees and trees with bounded degree, namely, we present and study gaps in AVL trees and we prove Tarjan et al.'s conjecture on the number of rotations in a sequence of deletions and insertions

Arbitrary weight changes in dynamic trees

We describe an implementation of dynamic weighted trees, called D-trees. Given a set left{ B_{0},...,B_{n}right} of objects and access frequencies q_{0},q_{1},...,q_{n} one wants to store the objects in a binary tree such that average access is nearly optimal and changes of the access frequencies require only small changes of the tree. In D-trees the changes are always limited to the path of search and hence update time is at most proportional to search time

A Smartphone-based Connected Vehicle Solution for Winter Road Surface Condition Monitoring

The monitoring of winter road surface conditions (RSCs) is essential to transportation agencies and the traveling public, since the former needs to be aware of the location and severity of existing RSCs in order to effectively maintain safe roadways with minimal environmental impact, while the latter uses RSC information to make informed travel decisions. However, current RSC monitoring practice still relies on methods that are time-consuming, labour-intensive and lacking in objectivity, therefore limiting their ability to provide sufficient spatial and temporal coverage across a road network. This research was motivated by the need for accurate, timely and reliable RSC monitoring for winter maintenance personnel and the travelling public. To achieve this objective, the field performance of a smartphone-based RSC monitoring system was evaluated on a section of Highway 6 in Ontario, Canada during the winter of 2014. A comparison between this system and current monitoring methods indicated that the former was capable of providing reliable results particularly at the maintenance route level; however, classification accuracy was found to vary according to RSC type. To improve the results produced by the smartphone-based system, this thesis proposes a connected- vehicle (CV) based RSC monitoring system that utilizes Road Weather Information System (RWIS) data in addition to the smartphone-based system’s data. Three techniques in artificial neural networks (ANNs), random trees (RTs), and random forests (RFs) were tested as the underlying models of the CV system, and the results indicated that all three models successfully increased the classification accuracy of the smartphone-based system. RFs were found to provide the most accurate RSC classifications for the standard (three-class) classification scheme while RTs were found to be most accurate when using a more detailed (five-class) classification scheme. Model transferability was also tested using data captured from a different test site during the winter of 2015; and it was found that although the proposed CV system significantly increased the reliability of RSC classifications, the underlying models were non-transferable and would therefore require local calibration before being used at different sites across a road network

Holland City News, Volume 84, Number 48: December 1, 1955

Newspaper published in Holland, Michigan, from 1872-1977, to serve the English-speaking people in Holland, Michigan. Purchased by local Dutch language newspaper, De Grondwet, owner in 1888.https://digitalcommons.hope.edu/hcn_1955/1047/thumbnail.jp

Evolving decision trees for the categorization of software

Current manual techniques of static reverse engineering are inefficient at providing semantic program understanding. An automated method to categorize applications was developed in order to quickly determine pertinent characteristics. Prior work in this area has had some success, but a major strength of the approach detailed in this thesis is that it produces heuristics that can be reused for quick analysis of new data. The method relies on a genetic programming algorithm to evolve decision trees which can be used to categorize software. The terminals, or leaf nodes, within the trees each contain values based on selected features from one of several attributes: system calls, byte N-grams, opcode N-grams, registers, opcode collocation, cyclomatic complexity, and bonding. The evolved decision trees are reusable and achieve average accuracies above 90% when categorizing programs based on compiler origin, authorship, and versions. Developing new decision trees simply requires more labeled datasets and potentially different feature selection algorithms for other attributes, depending on the data being classified. The genetic programming algorithm used to evolve the decision trees was compared against C4.5, a classic decision tree technique.In all experiments, the genetic programming approach outperformed C4.5. This thesis is an extension and expansion of the work published in the Computer Forensics in Software Engineering workshop at COMPSAC 2014 - the Annual 38th IEEE International Conference on Computer Software and Applications. This thesis is also being prepared as a journal article to be submitted for publication. --Abstract, page iii

Holland City News, Volume 84, Number 48: December 1, 1955

Newspaper published in Holland, Michigan, from 1872-1977, to serve the English-speaking people in Holland, Michigan. Purchased by local Dutch language newspaper, De Grondwet, owner in 1888.https://digitalcommons.hope.edu/hcn_1955/1047/thumbnail.jp