Algorithms for Multi-criteria One-Sided Boundary Labeling

Abstract

Abstract. We present new algorithms for labeling a set P of n points in the plane with labels that are aligned to the left of the bounding box of P . The points are connected to their labels by curves (leaders) that consist of two segments: a horizontal segment, and a second segment at a fixed angle with the first. Our algorithm finds a collection of nonintersecting leaders that minimizes the total number of bends, the total length, or any other 'badness' function of the leaders. An experimental evaluation of the performance is included.

Area-Feature Boundary Labeling

“…Benkert and Nöllenburg [8] presented algorithms for minimizing the total leader length with type-po or type-do 2 leaders, when uniform labels are allowed to be placed on one side of the enclosing rectangle. Recently, Benkert et al [9] studied boundary labeling along a new line of research.…”

“…Recently, Benkert et al [9] studied boundary labeling along a new line of research. They formulated the problem as an optimization problem, where the objective function is a general quality function which evaluates the niceness of the resulting labeling.…”

“…However, Benkert and Nöllenburg [8] and Benkert et al [9], report that the production of a boundary labeling with leaders of type do is not always feasible. This motivated Bekos, Kaufmann, Nöllenburg and Symvonis to introduce two new types of octilinear leaders and they further proved that by combining them, the boundary labeling problem is always feasible [10].…”

Boundary Labeling with Octilinear Leaders

“…Several authors have proposed algorithms to produce boundary labelings in different settings [2][3][4][5][6]11]. Recently, Benkert et al [5,6] studied the boundary labeling problem along a new line of research, according to which the leaders are of type do, i.e., polygonal lines consisting of two line segments, where the first one is "diagonal" to the side of R containing the label it leads to, whereas the second one is orthogonal to that side (see Figure 1c).…”

“…Recently, Benkert et al [5,6] studied the boundary labeling problem along a new line of research, according to which the leaders are of type do, i.e., polygonal lines consisting of two line segments, where the first one is "diagonal" to the side of R containing the label it leads to, whereas the second one is orthogonal to that side (see Figure 1c). Leaders of type do maintain a uniform shape and result in simple and easy-to-read labelings.…”