On computing the diameter of a point set in high dimensional Euclidean space

We consider the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space under Euclidean distance function. We describe an algorithm that in time $O(dnlog n +n^{2})$ finds with high probability an arbitrarily close approximation of the diameter. For large values of $d$ the complexity bound of our algorithm is a substantial improvement over the complexity bounds of previously known exact algorithms. Computing and approximating the diameter are fundamental primitives in high dimensional computational geometry and find practical application, for example, in clustering operations for image databases

Greedy Algorithms for Approximating the Diameter of Machine Learning Datasets in Multidimensional Euclidean Space: Experimental Results

Finding the diameter of a dataset in multidimensional Euclidean space is a well-established problem, with well-known algorithms. However, most of the algorithms found in the literature do not scale well with large values of data dimension, so the time complexity grows exponentially in most cases, which makes these algorithms impractical. Therefore, we implemented 4 simple greedy algorithms to be used for approximating the diameter of a multidimensional dataset; these are based on minimum/maximum l2 norms, hill climbing search, Tabu search and Beam search approaches, respectively. The time complexity of the implemented algorithms is near-linear, as they scale near-linearly with data size and its dimensions. The results of the experiments (conducted on different machine learning data sets) prove the efficiency of the implemented algorithms and can therefore be recommended for finding the diameter to be used by different machine learning applications when needed

A Deterministic Algorithm for the Three-Dimensional Diameter Problem

We give a deterministic algorithm for computing the diameter of an n point set in three dimensions with O(n log^c n) running time, c a constant