Open Problems for Iwoca 2007 1. Open Problems in Dynamic Map Labeling

Brief description The problem of map labeling is well-studied in GIS and computational geometry. The standard setting for such problems is the traditional (static) map. We are interested in dynamic maps, the sort we are familiar with on the web. The user can zoom and pan to view different portions of some large map that does not fit in the screen. One idea for solving dynamic labeling is to reduce them directly to static labeling. This is essentially the approach of Petzold [3, 4, 6, 5]. The problem with this approach is the consistency issue as pointed out by [1]. They listed a set of consistency desiderata, formalized the dynamic labeling problem. In particular, they introduce a natural class of dynamic placements called point-invariant placements which as a nice interpretation as a geometric cone (the third dimension is scale space). They also provided a practical solution satisfying the desiderata. This solution is implemented in the G-Vis System [2], a dynamic map for continental USA which is accessible by any browser. Since this problem is quite new, most issues are open. But here are two specific problems taken from [1]: 1. The solution in [1] assumes each label has a single placement. It should not be hard to generalize this to having a (small) finite set of discrete possibilities per label. More challenging is to accomodate labels with a continuous set of possibilities. 2. The complexity of the problem of active range optimization (ARO) in [1] is open. Intuitively, we can view a dynamic label as a cone (with a rectangular base) in 3-D. The problem is to truncate these cones so that they are non-overlapping subject to some optimization criteria. Recently, Sheung-Hung Poon (private communication) noted that the 1-D optimization version of the simplified ARO is polynomial-time, but the 2-D version remains open.