Force-Based Label Number Maximization

We present a force-based simulated annealing algorithm to heuristically solve 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 at its point-feature. The abstraction of the problem to the virtual force system allows us to implement additional aesthetic criteria and to compute placements with good label distribution in a short amount of time. Furthermore, our algorithm can be applied as a postprocessing step to improve existing labelings. We find that the results often look similar to those of a human cartographer. Extensive computational experiments on widely used benchmark data demonstrate that our new algorithm produces solutions where the number of placed labels is close to optimality and where the distribution of the labels is better than in labelings computed by algorithms that only maximize the number of placed labels. The experiments also show that the algorithm is able to solve large problems fast. This demonstrates its applicability in dynamic real-time environments, e.g., in navigation systems.