The increased availability of interactive maps on the Internet and on personal mobile devices has created new challenges in computational cartography and, in particular, for label placement in maps. Operations like rotation, zoom, and translation dynamically change the map over time and make a consistent adaptation of the map labeling necessary. In this paper, we consider map labeling for the case that a map undergoes a sequence of operations over a specified time span. We unify and generalize several preceding models for dynamic map labeling into one versatile and flexible model. In contrast to previous research, we completely abstract from the particular operations (e.g., zoom, rotation, etc.) and express the labeling problem as a set of time intervals representing the labels' presences, activities, and conflicts. The model's strength is manifested in its simplicity and broad range of applications. In particular, it supports label selection both for map features with fixed position as well as for moving entities (e.g., for tracking vehicles in logistics or air traffic control). Through extensive experiments on OpenStreetMap data, we evaluate our model using algorithms of varying complexity as a case study for navigation systems. Our experiments show that even simple (and thus, fast) algorithms achieve near-optimal solutions in our model with respect to an intuitive objective function.
In 2006, @cite_12 introduced the first formal model for dynamic maps and dynamic labels, formulating a general optimization problem. They described the change of a map by the operations , , and . In order to avoid and labels while transforming the map with zooming and panning, they required four desiderata for dynamic map labeling. These comprise , that labels should not vanish when zooming in or appear when zooming out (or any of the two when panning), , where label positions and size remain invariant during movement, and ---placement and selection of labels should be a function of the current map state only. Monotonicity was modeled as selecting for each label at most one scale interval, the so-called , during which the label is displayed. They introduced the (ARO) maximizing the sum of active ranges over all labels such that no two labels overlap and all desiderata are fulfilled. They proved that ARO is NP-hard for star-shaped labels and presented an optimal greedy algorithm for a simplified variant.
@cite_12
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We address the problem of filtering, selecting and placing labels on a dynamic map, which is characterized by continuous zooming and panning capabilities. This consists of two interrelated issues. The first is to avoid label popping and other artifacts that cause confusion and interrupt navigation, and the second is to label at interactive speed. In most formulations the static map labeling problem is NP-hard, and a fast approximation might have O(n log n) complexity. Even this is too slow during interaction, when the number of labels shown can be several orders of magnitude less than the number in the map. In this paper we introduce a set of desiderata for "consistent" dynamic map labeling, which has qualities desirable for navigation. We develop a new framework for dynamic labeling that achieves the desiderata and allows for fast interactive display by moving all of the selection and placement decisions into the preprocessing phase. This framework is general enough to accommodate a variety of selection and placement algorithms. It does not appear possible to achieve our desiderata using previous frameworks. Prior to this paper, there were no formal models of dynamic maps or of dynamic labels; our paper introduces both. We formulate a general optimization problem for dynamic map labeling and give a solution to a simple version of the problem. The simple version is based on label priorities and a versatile and intuitive class of dynamic label placements we call "invariant point placements". Despite these restrictions, our approach gives a useful and practical solution. Our implementation is incorporated into the G-Vis system which is a full-detail dynamic map of the continental USA. This demo is available through any browser