Analysis of Basic Data Reordering Techniques

Data reordering techniques are applied to improve the space and time efficiency of storage and query systems in various scientific and commercial applications. Run-length encoding is a prominent approach of compression in many areas, whose performance is significantly enhanced by achieving longer and fewer “runs” through data reordering. In this paper we theoretically study two reordering techniques, namely lexicographical order and Gray code order. We analyze these two methods in the context of bitmap indexes, which are known to have high query performances. We take into account the two commonly used bitmap encodings: equality and range. Our analysis indicates that, when we have all the possible data tuples, both ordering methods perform the same with equality encoding. However, Gray code achieves better compression with range encoding. Experimental results are provided to validate the theoretical analysis.