An FPTAS for computing the similarity of three-dimensional point sets

We present an FPTAS for a combinatorial optimization problem which is motivated a problem in drug-design. The problem is as follow. One is given two finite subsets A, B of points in three-dimensional space which represent the centers of atoms of two molecules. The objective function is large if there are an appropriate rigid motion M, subset S subset of A and T subset of B of the same size and a bijective function f from S to M(T) such that vertical bar S vertical bar is sufficiently large and the root mean squared distance between S and f(S) is small. The object is to find M and f such that the objective function is maximized. The corresponding maximum value defines the similarity score between two molecules.