Mixed map labeling

Point feature map labeling is a geometric visualization problem, in which a set of input points must be labeled with a set of disjoint rectangles (the bounding boxes of the label texts). It is predominantly motivated by label placement in maps but it also has other visualization applications. Typically, labeling models either use internal labels, which must touch their feature point, or external (boundary) labels, which are placed outside the input image and which are connected to their feature points by crossing-free leader lines. In this paper we study polynomial-time algorithms for maximizing the number of internal labels in a mixed labeling model that combines internal and external labels. The model requires that all leaders are parallel to a given orientation θ ∈ [0, 2π), the value of which influences the geometric properties and hence the running times of our algorithms