The label placement problem is one of the most important problems in geographic information systems, cartography, graph drawing, and graphical interface design. In this paper, we considered the label size maximization problem for points with axes-parallel rectangular labels that correspond to character strings and have different widths based on the number of characters. We propose an algorithm for computing the optimum size for the label size maximization problem in the 2-position model and a polynomial time algorithm for the problem in the 4-position model. Our algorithm cannot obtain the maximum value in the 4-position model because the label size maximization problem in the 4-position model is NP-hard. However, our algorithm is efficient in practice, as shown by computational experiments. Further, computational results for JR trains, subways and major private railroads in Tokyo are presented.

The label placement problem is one of the most important problems in geographic information systems, cartography, graph drawing and graphical interface design. In this paper, we consider the problem of labeling points and curves in maps drawn from digital data. In digital maps, a curve is represented as a set of points and consists of many small segments. The label for each curve must be placed alongside the corresponding curve. We define a continuous labeling space for points and curves, and present an algorithm using this space for positioning labels. Computational results for subway and JR train maps in Tokyo are presented.