A new method for planar graph drawings on a grid (abstract)

Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows: (i) We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. (ii) We present several efficient dynamic drawing algorithms for trees, series-parallel digraphs, planar st-digraphs, and planar graphs. These algorithms adopt a variety of representations (e.g., straight-line, polyline, visibility), and update the drawing in a smooth way. (iii) We show that the implicit representation of the layout used by our algorithms for trees and series-parallel digraphs also supports point-location and window queries. (Joint work with P. Bertolazzi, G. Di Battista, R. Tamassia, and I. G. Tollis.)