### Abstract

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.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 575-587 |

Number of pages | 13 |

Volume | 2518 LNCS |

DOIs | |

State | Published - 2002 |

Event | 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 - Vancouver, BC, Canada Duration: Nov 21 2002 → Nov 23 2002 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2518 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 |
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Country | Canada |

City | Vancouver, BC |

Period | 11/21/02 → 11/23/02 |

### Fingerprint

### Keywords

- Convex planar drawing
- Graph drawing
- Planar embedding
- Simultaneous embedding

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 2518 LNCS, pp. 575-587). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2518 LNCS). https://doi.org/10.1007/3-540-36136-7_50

**Simultaneous embedding of a planar graph and its dual on the grid.** / Erten, Cesim; Kobourov, Stephen G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 2518 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2518 LNCS, pp. 575-587, 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002, Vancouver, BC, Canada, 11/21/02. https://doi.org/10.1007/3-540-36136-7_50

}

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

SN - 3540001425

SN - 9783540001423

VL - 2518 LNCS

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

SP - 575

EP - 587

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

ER -