Elastic Labels on the Perimeter of a Rectangle
An important and challenging task in cartography is the labeling of maps-attaching text to geographic features. Usually, the features to be labeled are regions, lines, and points on a map. One of the traditional formulations of the problem of labeling points is the point-feature-label placement problem, where we are given a set of points in the plane, and an axis-parallel rectangular label associated with each point, and the problem is to place each label with one corner at its associated point such that no two labels overlap. [KIm88, FWa91, MSh91, KRa92] This problem is known to be NP-complete. There are approximation algorithms when the problem consists of scaling the labels.
KeywordsApproximation Algorithm Polynomial Time Algorithm Traditional Formulation Packing Problem Geographic Feature
- [FWa91]M. Formann and F. Wagner. A packing problem with applications in lettering of maps. Proceedings of the 7th ACM Symposium on Computational Geometry. (1991) 281–288.Google Scholar
- [KIm88]T. Kato and H. Imai. The NP-completeness of the character placement problem of 2 or 3 degrees of freedom. Record of Joint Conference of Electrical and Electronic engineers in Kyushu. (1988), 1138. In Japanese.Google Scholar
- [ILu97a]C. Iturriaga and A. Lubiw. NP-hardness of some map labeling problems. Technical Report CS-97-18. University of Waterloo (1997).Google Scholar
- [MSh91]J. Marks and S. Shieber. The computational complexity of cartographic label placement. Technical Report CRCT-05-91. Harvard University (1991).Google Scholar