Adaptive zooming in point set labeling

A set of points shown on the map usually represents special sites like cities or towns in a country. If the map in the interactive geographical information system (GIS) is browsed by users on the computer screen or on the web, the points and their labels can be viewed in a query window at different resolutions by zooming in or out according to the users' requirements. How can we make use of the information obtained from different resolutions to avoid doing the whole labeling from scratch every time the zooming factor changes? We investigate this important issue in the interactive GIS system. In this paper, we build low-height hierarchies for one and two dimensions so that optimal and approximating solutions for adaptive zooming queries can be answered efficiently. To the best of our knowledge, no previous results have been known on this issue with theoretical guarantees.