This paper is concerned with the problem of computing coverings of a set of colored points in a plane (I personally find the title slightly misleading). In particular, the initial data consists of a set of points in the plane that are colored with colors from a given set of colors. The problems investigated are then certain “optimal hull problems,” like finding the smallest circle enclosing a set of points containing a least one point of each color.

The main results of the paper are new algorithms that do not need prior computations of Voronoi diagrams and/or give better approximations than currently known results.

The paper starts with an overview of existing literature on the problem and a layout of the main results and how they are going to be presented. This is followed by some basic definitions needed for understanding the rest of the discussion.

The main body of the paper consists of three sections presenting the algorithms and the mathematical proof of their properties.

The paper is understandable, although some language glitches might cause some confusion. The diagrams greatly help in understanding the ideas. Some information on the practical relevance of the work would have been nice. I could not get a feeling on whether the improvement in approximation really makes a difference or whether the presented algorithms are as equally easy to implement as the existing ones.