A simple linear algorithm for computing rectilinear 3-centers

Rectilinear k-centers of a finite point set P⊂R2 are the centers of at most k congruent axis-parallel squares of minimal size whose union covers P. This paper describes a linear time algorithm based on the prune-and-search paradigm to compute rectilinear 3-centers. The algorithm is elementary in the sense that it does not build on any sophisticated data structures or other algorithms, except for linear time median finding. An implementation is publically available as part of the Computational Geometry Algorithms Library (Cgal).