TY - JOUR

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

AU - Erten, Cesim

AU - Kobourov, Stephen G.

N1 - Funding Information:
∗ This research was partially supported by NSF Grant ACR-0222920.

PY - 2005/5

Y1 - 2005/5

N2 - Traditional representations of graphs and their duals suggest that the dual vertices should be placed inside their corresponding primal faces, and the edges of the dual graph should only cross 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. All the edges are drawn as straight-line segments except for one edge on the outer face, which is drawn using two segments.

AB - Traditional representations of graphs and their duals suggest that the dual vertices should be placed inside their corresponding primal faces, and the edges of the dual graph should only cross 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. All the edges are drawn as straight-line segments except for one edge on the outer face, which is drawn using two segments.

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U2 - 10.1007/s00224-005-1143-4

DO - 10.1007/s00224-005-1143-4

M3 - Article

AN - SCOPUS:18244373185

VL - 38

SP - 313

EP - 327

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 3

ER -