Mixed Map Labeling

TL;DR

This paper investigates polynomial-time algorithms for optimizing mixed map labeling, balancing internal and external labels with leader lines oriented at a fixed angle, to improve labeling efficiency.

Contribution

It introduces algorithms for maximizing internal labels in a mixed labeling model with fixed leader orientations, combining internal and external label placement strategies.

Findings

Algorithms depend on the orientation angle θ.

Polynomial-time solutions are provided for the mixed labeling problem.

The model balances internal and external labels effectively.

Abstract

Point feature map labeling is a geometric problem, in which a set of input points must be labeled with a set of disjoint rectangles (the bounding boxes of the label texts). Typically, labeling models either use internal labels, which must touch their feature point, or external (boundary) labels, which are placed on one of the four sides of the input points' bounding box 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 $\theta \in [0,2\pi)$, whose value influences the geometric properties and hence the running times of our algorithms.