An Extended Symbolic-Arithmetic Model for Teaching Double-Black Removal with Rotation in Red-Black Trees

Double-black (DB) nodes have no place in red-black (RB) trees. So when DB nodes are formed, they are immediately removed. The removal of DB nodes that cause rotation and recoloring of other connected nodes poses greater challenges in the teaching and learning of RB trees. To ease this difficulty, this paper extends our previous work on the symbolic arithmetic algebraic (SA) method for removing DB nodes. The SA operations that are given as, Red + Black = Black; Black - Black = Red; Black + Black = DB; and DB - Black = Black removes DB nodes and rebalances black heights in RB trees. By extension, this paper projects three SA mathematical equations, namely, general symbolic arithmetic rule; partial symbolic arithmetic rule1; and partial symbolic arithmetic rule2. The removal of a DB node ultimately affects black heights in RB trees. To balance black heights using the SA equations, all the RB tree cases, namely, LR, RL, LL, and RR, were considered in this work; and the position of the nodes connected directly or indirectly to the DB node was also tested. In this study, to balance a RB tree, the issues considered w.r.t. the different cases of the RB tree were i) whether a DB node has an inner, outer, or both inner and outer black nephews; or ii) whether a DB node has an inner, outer or both inner and outer red nephews. The nephews r and x in this work are the children of the sibling s to a DB, and further up the tree, the parent p of a DB is their grandparent g. Thus, r and x have indirect relationships to a DB at the point of formation of the DB node. The novelty of the SA equations is in their effectiveness in the removal of DB that involves rotation of nodes as well as the recoloring of nodes along any simple path so as to balance black heights in a tree.

Design and Analysis of a Multi-Agent E-Learning System Using Prometheus Design Tool

Agent unified modeling languages (AUML) are agent-oriented approaches that supports the specification, design, visualization and documentation of an agent-based system. This paper presents the use of Prometheus AUML approach for the modeling of a Pre-assessment System of five interactive agents. The Pre-assessment System, as previously reported, is a multi-agent based e-learning system that is developed to support the assessment of prior learning skills in students so as to classify their skills and make recommendation for their learning. This paper discusses the detailed design approach of the system in a step-by-step manner; and domain knowledge abstraction and organization in the system. In addition, the analysis of the data collated and models of prediction for future pre-assessment results are also presented.

Computational Estimate Visualisation and Evaluation of Agent Classified Rules Learning System

Student modelling and agent classified rules learning as applied in the development of the intelligent Preassessment System has been presented in [10],[11]. In this paper, we now demystify the theory behind the development of the pre-assessment system followed by some computational experimentation and graph visualisation of the agent classified rules learning algorithm in the estimation and prediction of classified rules. In addition, we present some preliminary results of the pre-assessment system evaluation. From the results, it is gathered that the system has performed according to its design specification.

A system of serial computation for classified rules prediction in non-regular ontology trees

Objects or structures that are regular take uniform dimensions. Based on the concepts of regular models, our previous research work has developed a system of a regular ontology that models learning structures in a multiagent system for uniform pre-assessments in a learning environment. This regular ontology has led to the modelling of a classified rules learning algorithm that predicts the actual number of rules needed for inductive learning processes and decision making in a multiagent system. But not all processes or models are regular. Thus this paper presents a system of polynomial equation that can estimate and predict the required number of rules of a non-regular ontology model given some defined parameters.