Narrow Results

A rectilinear map consists of a set of mutually non-intersecting rectilinear (i.e., horizontal or vertical) line segments, and each segment is allowed to use a rectangular label of height B and length the same as the segment. Sliding labels are not restricted to any finite number of predefined positions but can slide and be placed at any position as long as it intersects the segment. This paper considers three versions of the problem of labeling a rectilinear map with sliding labels and presents efficient exact and approximation algorithms for them.

Driven by the industrial challenge of labeling maps for GIS applications, we investigate the problem of computing a map region P such that a rectangular axis-parallel label L of a given size can be placed in it. The map region to be labeled is in general a non-convex n-gon which may contain holes. We first derive a new practical algorithm based on the sweep-line technique that determines the com set of Maximum Inscribed Rectangles (MIRs) in P in O(nk), where k is the size of the output, for the case when the polygon sides have an axis-parallel orientation. After the set of MIRs has been found, any subsequent query on label L placement runs in only O(logn) time. We then provide an algorithm to convert the general case to the axis-parallel case. Extensive experimentation in both laboratory and industrial settings confirms that the developed method is practical and highly efficient for processing large GIS data sets.