Matching points with squares

Abstract

Given a class C of geometric objects and a point set P, a C -matching of P is a set M={C1,.,.,.Ck ⊂ C of elements of C such that each C i contains exactly two elements of P and each element of P lies in at most one C i . If all of the elements of P belong to some C i , M is called a perfect matching. If, in addition, all of the elements of M are pairwise disjoint, we say that this matching M is strong. In this paper we study the existence and characteristics of C -matchings for point sets in the plane when C is the set of isothetic squares in the plane. A consequence of our results is a proof that the Delaunay triangulations for the L ∞ metric and the L 1 metric always admit a Hamiltonian path. © 2008 Springer Science+Business Media, LLC.