Efficient Approximation Algorithms for Two-Label Point Labeling

In this paper we propose and study two practical variations of the map labeling problem: Given a set S of n distinct (point) sites in the plane, label each site with: (1) a pair of non-intersecting squares of maximum possible size, (2) a pair of non-intersecting circles of maximum possible size (all the squares and circles are topologically open and are of uniform size). Almost nothing has been done before in this aspect, i.e., multi-label map labeling. We obtain constant-factor approximation algorithms for these problems. We also study bicriteria approximation schemes for these problems under a mild condition.