Dynamic indexing for multidimensional non-ordered discrete data spaces using a data-partitioning approach

Abstract

Similarity searches in multidimensional Non-ordered Discrete Data Spaces (NDDS) are becoming increasingly important for application areas such as bioinformatics, biometrics, data mining and E-commerce. Efficient similarity searches require robust indexing techniques. Unfortunately, existing indexing methods developed for multidimensional (ordered) Continuous Data Spaces (CDS) such as the R-tree cannot be directly applied to an NDDS. This is because some essential geometric concepts/properties such as the minimum bounding region and the area of a region in a CDS are no longer valid in an NDDS. Other indexing methods based on metric spaces such as the M-tree and the Slim-trees are too general to effectively utilize the special characteristics of NDDSs, resulting in nonoptimized performance. In this article, we propose a new dynamic data-partitioning-based indexing technique, called the ND-tree, to support efficient similarity searches in an NDDS. The key idea is to extend the relevant geometric concepts as well as some indexing strategies used in CDSs to NDDSs. Efficient algorithms for ND-tree construction and techniques to solve relevant issues such as handling dimensions with different alphabets in an NDDS are presented. Our experimental results on synthetic data and real genome sequence data demonstrate that the ND-tree outperforms the linear scan, the M-tree and the Slim-trees for similarity searches in multidimensional NDDSs. A theoretical model is also developed to predict the performance of the ND-tree for random data.