An Efficient Implementation Scheme for Multidimensional Index Array Operations and its Evaluation

Abstract

Multidimensional arrays are greatly used for handling large amount of data in scientific or engineering, and Database applications. Most of the on hand data structures are static in nature. We describe a novel implementation idea of multidimensional array for handling such large scale datasets. The scheme implements a dynamic multidimensional extendible array employing a set of two dimensional extendible arrays. The Traditional Multidimensional Array (TMA) or Extended Karnaugh Map Represented (EKMR) array is an efficient structure in terms of accessing the element of the array by straight computation of the addressing function, but they are not extendible during run time. But real world data grows in incremental fashion. So, there is strong demand of data structure that is dynamically extendible during run time. Three are some extendible array models, most of which uses a concept of extension subarray. For n-dimensional array the subarrays are n-1 dimensional. But, if the length of dimension and/or number of dimension of a multidimensional array is large then the address space, even for the subarray, overflows the machine limit very soon. Another issue for representing the real life data by multidimensional arrays is that it creates a problem of high degree of sparsity and need to be compressed. It is therefore desirable to develop techniques that can access the data in their compressed form and can perform logical operations directly on the compressed data. In this research work we propose a data structure using the idea of EKMR and Traditional Extendible Array, namely Extendible Karnaugh Array (EKA) to represent the multidimensional data. The scheme has the intuitive propensity against the essential problem of address space overflow as well as it can be extended in any direction during run time. Moreover, we present a compression scheme for EKA to facilitate data access in compressed form. We evaluate our proposed scheme by comparing for different retrieval and extension operations with the Traditional Multidimensional Array (TMA). Our experimental result shows that the EKA scheme has a significant delay on the occurrence of address space overflow without any performance penalty. Furthermore, we find that range of usability of the compression scheme is independent of length or number of dimension. And it is better to use compressed EKA rather than uncompressed EKA for representing sparse data sets which needs range retrieval frequently.