Prime Number-Based Hierarchical Data Labeling Scheme for Relational Databases

Abstract

Hierarchical data structures are an important aspect of many computer science fields including data mining, terrain modeling, and image analysis. A good representation of such data accurately captures the parent-child and ancestor-descendent relationships between nodes. There exist a number of different ways to capture and manage hierarchical data while preserving such relationships. For instance, one may use a custom system designed for a specific kind of hierarchy. Object oriented databases may also be used to model hierarchical data. Relational database systems, on the other hand, add an additional benefit of mature mathematical theory, reliable implementations, superior functionality and scalability. Relational databases were not originally designed with hierarchical data management in mind. As a result, abstract information can not be natively stored in database relations. Database labeling schemes resolve this issue by labeling all nodes in a way that reveals their relationships. Labels usually encode the node's position in a hierarchy as a number or a string that can be stored, indexed, searched, and retrieved from a database. Many different labeling schemes have been developed in the past. All of them may be classified into three broad categories: recursive expansion, materialized path, and nested sets. Each model has its strengths and weaknesses. Each model implementation attempts to reduce the number of weaknesses inherent to the respective model. One of the most prominent implementations of the materialized path model uses the unique characteristics of prime numbers for its labeling purposes. However, the performance and space utilization of this prime number labeling scheme could be significantly improved. This research introduces a new scheme called reusable prime number labeling (rPNL) that reduces the effects of the mentioned weaknesses. The proposed scheme advantage is discussed in detail, proven mathematically, and experimentally confirmed.