Traditional representations of graphs and their duals suggest the requirement that the dual vertices should be placed inside their corresponding primal faces, and the edges of the dual graph should cross only their corresponding primal edges. We consider the problem of simultaneously embedding a planar graph and its dual on a small integer grid such that the edges are drawn as straight-line segments and the only crossings are between primal-dual pairs of edges. We provide an O(n) time algorithm that simultaneously embeds a 3-connected planar graph and its dual on a (2n - 2) × (2n - 2) integer grid, where n is the total number of vertices in the graph and its dual. © Springer-Verlag Berlin Heidelberg 2002.
CITATION STYLE
Erten, C., & Kobourov, S. G. (2002). Simultaneous embedding of a planar graph and its dual on the grid. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2518 LNCS, pp. 575–587). https://doi.org/10.1007/3-540-36136-7_50
Mendeley helps you to discover research relevant for your work.