An efficient implementation of distance-based diversity measures based on k-d trees

The problem of quantifying molecular diversity continues to attract significant interest among computational chemists. Most algorithms reported to date are distance-based and scale to the square of the size of the data set. This paper reports an alternative algorithm based on k-dimensional (or k-d) trees. k-d trees are combinatorial data structures that allow expedient location of nearest neighbors in multivariate spaces. Nearest neighbor detection forms the basis of many popular diversity measures, such as maximin, minimum spanning trees, and many others. In this report, we demonstrate that k-d trees exhibit excellent scaling characteristics and can be used to accelerate diversity estimation without compromising the quality of the design. The advantages of this approach are contrasted with an alternative algorithm that was recently proposed by Turner et al. based on the cosine similarity coefficient.