TY - GEN

T1 - Simultaneous embedding of a planar graph and its dual on the grid

AU - Erten, Cesim

AU - Kobourov, Stephen G.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - Convex planar drawing

KW - Graph drawing

KW - Planar embedding

KW - Simultaneous embedding

UR - http://www.scopus.com/inward/record.url?scp=84878641539&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878641539&partnerID=8YFLogxK

U2 - 10.1007/3-540-36136-7_50

DO - 10.1007/3-540-36136-7_50

M3 - Conference contribution

AN - SCOPUS:84878641539

SN - 3540001425

SN - 9783540001423

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 575

EP - 587

BT - Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings

T2 - 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002

Y2 - 21 November 2002 through 23 November 2002

ER -