dominatingSampling

Dominating sampling is a technique used in computational geometry and related fields to select a subset of points from a larger set in a way that ensures certain properties are maintained or approximated. The core idea is to choose a subset of points, called the "dominating set," such that each point not in the dominating set is "close" to at least one point within the dominating set. The definition of "close" depends on the specific application, but it often refers to being within a certain distance or sharing a particular characteristic.

This sampling method is particularly useful when dealing with large datasets where processing every single point is computationally infeasible. By selecting a representative dominating set, algorithms can operate on this smaller subset while still achieving results that are statistically similar or bounded with respect to the original, larger set. It's a form of data reduction that aims to preserve essential spatial or structural information.

Applications of dominating sampling can be found in areas such as clustering, nearest neighbor search, and point set simplification. For example, in clustering, a dominating set might be used to identify initial cluster centroids. In nearest neighbor search, it can help to quickly prune the search space. The effectiveness of dominating sampling often depends on the distribution of the points and the chosen metric for defining "closeness." Various algorithms exist for constructing dominating sets, each with different trade-offs in terms of the size of the dominating set and the quality of the approximation.