Algorithms for Labeling Focus Regions

In this paper, we investigate the problem of labeling point sites in focus regions of maps or diagrams. This problem occurs, for example, when the user of a mapping service wants to see the names of restaurants or other POIs in a crowded downtown area but keep the overview over a larger area. Our approach is to place the labels at the boundary of the focus region and connect each site with its label by a linear connection, which is called a leader. In this way, we move labels from the focus region to the less valuable context region surrounding it. In order to make the leader layout well readable, we present algorithms that rule out crossings between leaders and optimize other characteristics such as total leader length and distance between labels. This yields a new variant of the boundary labeling problem, which has been studied in the literature. Other than in traditional boundary labeling, where leaders are usually schematized polylines, we focus on leaders that are either straight-line segments or Bezier curves. Further, we present algorithms that, given the sites, find a position of the focus region that optimizes the above characteristics. We also consider a variant of the problem where we have more sites than space for labels. In this situation, we assume that the sites are prioritized by the user. Alternatively, we take a new facility-location perspective which yields a clustering of the sites. We label one representative of each cluster. If the user wishes, we apply our approach to the sites within a cluster, giving details on demand.