An empirical study of algorithms for point-feature label placement

Abstract

A major factor affecting the clarity of graphical displays that include text labels is the degree to which labels obscure display features (including other labels) as a result of spatial overlap. Point-feature label placement (PFLP) is the problem of placing text labels adjacent to point features on a map or diagram so as to maximize legibility. This problem occurs frequently in the production of many types of informational graphics, though it arises most often in automated cartography. In this paper we present a comprehensive treatment of the PFLP problem, viewed as a type of combinatorial optimization problem. Complexity analysis reveals that the basic PFLP problem and most interesting variants of it are NP-hard. These negative results help inform a survey of previously reported algorithms for PFLP; not surprisingly, all such algorithms either have exponential time complexity or are incomplete. To solve the PFLP problem in practice, then, we must rely on good heuristic methods. We propose two new methods, one based on a discrete form of gradient descent, the other on simulated annealing, and report on a series of empirical tests comparing these and the other known algorithms for the problem. Based on this study, the first to be conducted, we identify the best approaches as a function of available computation time.

A Combinatorial Framework for Map Labeling

“…Given heaps and priority search trees, it would run faster. Our implementation of simulated annealing seems to be slower by a factor of 2 to 3 than that of Christiansen et al [CMS95]. This difference in running time may be due to the machines on which the times were measured.…”

“…The simulated annealing algorithm we used relies on the experiments performed by Christensen et al and follows their suggestions for the initial configuration, the objective function, a method for generating configuration changes, and the annealing schedule [CMS95]. In order to save time, we allowed only 30 instead of the proposed 50 temperature stages in the annealing schedule.…”

“…VariableDensity. This example class is used in the experimental paper by Christensen et al [CMS95]. There the points are distributed uniformly on a rectangle of size 792 × 612.…”

“…Our tests differ from experiments performed by other researchers [Hir82,CMS95,CFMS97,vKSW98,KT98] in that we included example classes where we could measure our results with respect to tight bounds on the optimal solution.…”

Dynamic Topography Information Landscapes – An Incremental Approach to Visual Knowledge Discovery

“…The resulting landscape surface image resembles a geographic map with peaks at areas, where document density is large, and oceans or valleys, where document density is low. Finally, a heuristic point feature label placement algorithm [6] is used with the labeling quality evaluation in the following basic rules: (i) No overlap of a label with other labels and the image boundary.…”