Label Number Maximization in the Slider Model

We consider the NP-hard label number maximization problem lnm: Given a set of rectangular labels, each of which belongs to a point feature in the plane, the task is to find a labeling for a largest subset of the labels. A labeling is a placement such that none of the labels overlap and each is placed so that its boundary touches the corresponding point feature. The purpose of this paper is twofold: We present a new force-based simulated annealing algorithm to heuristically solve the problem and we provide the results of a very thorough experimental comparison of the best known labeling methods on widely used benchmark sets. The design of our new method has been guided by the goal to produce labelings that are similar to the results of an experienced human performing the same task. So we are not only looking for a labeling where the number of labels placed is high but also where the distribution of the placed labels is good. Our experimental results show that the new algorithm outperforms the other methods in terms of quality while still being reasonably fast and confirm that the simulated annealing method is well-suited for map labeling problems.