An FPTAS for Computing the Similarity of Three-Dimensional Point Sets

We present an FPTAS for a combinatorial optimization problem which is motivated by a problem in drug-design. The problem is as follows. 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 , subsets S ⊂ A and T ⊂ B of the same size and a bijective function f from S to M(T ) such that |S| 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.