Multi-page Labeling of Small-screen Maps with a Graph-coloring Approach

Annotating small-screen maps with additional content such as labels for points of interest is a highly challenging problem that requires new algorithmic solutions. A common labeling approach is to select a maximum-size subset of all labels such that no two labels constitute a graphical conflict and to display only the selected labels in the map. A disadvantage of this approach is that a user often has to zoom in and out repeatedly to access all points of interest in a certain region. Since this can be very cumbersome, we suggest an alternative approach that allows the scale of the map to be kept fixed. Our approach is to distribute all labels on multiple pages through which the user can navigate, for example, by swiping the pages from right to left. We in particular optimize the assignment of the labels to pages such that no page contains two conflicting labels, more important labels appear on the first pages, and sparsely labeled pages are avoided. Algorithmically, we reduce this problem to a weighted and constrained graph coloring problem based on a graph representing conflicts between labels such that an optimal coloring of the graph corresponds to a multi-page labeling. We propose a simple greedy heuristic that is fast enough to be deployed in web-applications. We evaluate the quality of the obtained labelings by comparing them with optimal solutions, which we obtain by means of integer linear programming formulations. In our evaluation on real-world data we particularly show that the proposed heuristic achieves near-optimal solutions with respect to the chosen objective function and that it substantially improves the legibility of the labels in comparison to the simple strategy of assigning the labels to pages solely based on the labels’ weights.