Empirical testing of algorithms for variable-sized label placement

Abstract

The development of methods for placing labels on map features is a central problem in automated cartography. A well-studied problem of this sort is the point-feature label placement (PFLP) problem: Given a set of points and a set of candidate label positions adjacent to each point tind the choice of label position for each point that minimizes the total number of label-label and label-point overlaps. Sample labelings of th~ sort are depicted in Figure 1. This NPhard problem has been attacked by a number of researchers. Thorough empirical testing has shown that a heuristic algorithm baaed on simulated annealing (SA) outperforms all previously published practical algorithms for this problem [1]. Recently, Wagner and Wolff [3] have explored a variant of the PFLP problem. In their problem, which we call var-iablesized point-feature label placement (VPFLP), the goal is to find the largest label scale at which the set of points can be labeled with zero overlaps; that is, only perfect labelings are allowed, but the size of the labels is allowed to vary uniformly. (See Figure 1.) Wagner and Wolff present an afgorithm for the specific case of VPFLP in which each point has four candidate label positions (4-VPFLP). Wagner and Wolff do not compare their own algorithm for this problem with those of other researchers. In this note, we report on empirical testing of Wagner and Wolff’s algorithm (which we will refer to = WW) for 4-VPFLP with the SA algorithm. We find that SA performs essentially identically to WW, though it is slower. However, the generality of the SA algorithm (explored, for instance, by Edmondson et al. [2]) means that, unlike WW, SA can be applied to a far broader range of VPFLP variants. Finally, we address the question of whether the clever preprocessing method used in WW might be advantageously applied to PFLP by using it as a preprocessing step for SA, and show that it provides no advantage. The WW algorithm for VPFLP works by performing a simple binary search over scales; at each candidate scale, a