A universal algorithm for finding the shortest distance between systems of points

Abstract

Three universal algorithms for geometrical comparison of abstract sets of n points in the Euclidean space R 3 are proposed. It is proved that at an accuracy ∊ the efficiency of all the algorithms does not exceed O(n 3/∊3/2). The most effective algorithm combines the known Hungarian and Kabsch algorithms, but is free of their deficiencies and fast enough to match hundreds of points. The algorithm is applied to compare both finite (ligands) and periodic (nets) chemical objects.