Algorithmic Aspects of Proportional Symbol Maps [chapter]

S. Cabello, H. Haverkort, M. van Kreveld, B. Speckmann
2006 Lecture Notes in Computer Science  
Proportional symbol maps visualize numerical data associated with point locations by placing a scaled symbol-typically opaque disks or squares-at the corresponding point on a map. Overlapping symbols need to be drawn in such a way that the user can still judge their relative sizes accurately. We identify two types of suitable drawings: physically realizable drawings and stacking drawings. For these we study the following two problems: Max-Min-maximize the minimum visible boundary length of each
more » ... symbol-and Max-Total-maximize the total visible boundary length over all symbols. We show that both problems are NP-hard for physically realizable drawings. Max-Min can be solved in O(n 2 log n) time for stacking drawings, which can be improved to O(n log n) or O(n log 2 n) time when the input has certain properties. We also experimented with four methods to compute stacking drawings: our solution to the Max-Min problem performs best on the data sets considered.
doi:10.1007/11841036_64 fatcat:z4frf5smd5hv3lpqyyx3hk5vmi