$N$ -Dimensional Approximation of Euclidean Distance

Abstract

Several applications in different engineering areas require the computation of the Euclidean distance, a quite complex operation based on squaring and square root. In some applications, the Euclidean distance can be replaced by the Manhattan distance. However, the approximation error introduced by the Manhattan distance may be rather large, especially in a multi-dimensional space, and may compromise the overall performance. In this brief, we propose an extension of the αMax+βMin method to approximate the Euclidean distance to a multi-dimensional space. Such a method results in a much smaller approximation error with respect to the Manhattan approximation at the expense of a reasonable increase in hardware cost. Moreover, with respect to the Euclidean distance, the αMax+βMin method provides a significant reduction in the hardware if the application can tolerate some errors.