Algorithms for point set matching with k-differences

Abstract

The largest common point set problem (LCP) is, given two point set P and Q in d-dimensional Euclidean space, to find a subset of P with the maximum cardinality that is congruent to some subset of Q. We consider a special case of LCP in which the size of the largest common point set is at least (|P| + |Q| - k)/2. We develop efficient algorithms for this special case of LCP and a related problem. In particular, we present an O(k3n1.34 + kn2 log n) time algorithm for LCP in two dimensions, which is much better for small k than an existing O(n3.2 log n) time algorithm, where n = max{|P|,|Q|}. © Springer-Verlag Berlin Heidelberg 2004.