### Abstract

Universal pointsets can be used for visualizing multiple relationships on the same set of objects or for visualizing dynamic graph processes. In simultaneous geometric embeddings, the same point in the plane is used to represent the same object as a way to preserve the viewer's mental map. In colored simultaneous embeddings this restriction is relaxed, by allowing a given object to map to a subset of points in the plane. Specifically, consider a set of graphs on the same set of n vertices partitioned into k colors. Finding a corresponding set of k-colored points in the plane such that each vertex is mapped to a point of the same color so as to allow a straightline plane drawing of each graph is the problem of colored simultaneous geometric embedding.

Original language | English (US) |
---|---|

Pages (from-to) | 569-592 |

Number of pages | 24 |

Journal | Algorithmica |

Volume | 60 |

Issue number | 3 |

DOIs | |

State | Published - Jul 2011 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics

### Cite this

*Algorithmica*,

*60*(3), 569-592. https://doi.org/10.1007/s00453-010-9433-x

**Colored simultaneous geometric embeddings and universal pointsets.** / Brandes, Ulrik; Erten, Cesim; Estrella-Balderrama, Alejandro; Fowler, J. Joseph; Frati, Fabrizio; Geyer, Markus; Gutwenger, Carsten; Hong, Seok Hee; Kaufmann, Michael; Kobourov, Stephen G; Liotta, Giuseppe; Mutzel, Petra; Symvonis, Antonios.

Research output: Contribution to journal › Article

*Algorithmica*, vol. 60, no. 3, pp. 569-592. https://doi.org/10.1007/s00453-010-9433-x

}

TY - JOUR

T1 - Colored simultaneous geometric embeddings and universal pointsets

AU - Brandes, Ulrik

AU - Erten, Cesim

AU - Estrella-Balderrama, Alejandro

AU - Fowler, J. Joseph

AU - Frati, Fabrizio

AU - Geyer, Markus

AU - Gutwenger, Carsten

AU - Hong, Seok Hee

AU - Kaufmann, Michael

AU - Kobourov, Stephen G

AU - Liotta, Giuseppe

AU - Mutzel, Petra

AU - Symvonis, Antonios

PY - 2011/7

Y1 - 2011/7

N2 - Universal pointsets can be used for visualizing multiple relationships on the same set of objects or for visualizing dynamic graph processes. In simultaneous geometric embeddings, the same point in the plane is used to represent the same object as a way to preserve the viewer's mental map. In colored simultaneous embeddings this restriction is relaxed, by allowing a given object to map to a subset of points in the plane. Specifically, consider a set of graphs on the same set of n vertices partitioned into k colors. Finding a corresponding set of k-colored points in the plane such that each vertex is mapped to a point of the same color so as to allow a straightline plane drawing of each graph is the problem of colored simultaneous geometric embedding.

AB - Universal pointsets can be used for visualizing multiple relationships on the same set of objects or for visualizing dynamic graph processes. In simultaneous geometric embeddings, the same point in the plane is used to represent the same object as a way to preserve the viewer's mental map. In colored simultaneous embeddings this restriction is relaxed, by allowing a given object to map to a subset of points in the plane. Specifically, consider a set of graphs on the same set of n vertices partitioned into k colors. Finding a corresponding set of k-colored points in the plane such that each vertex is mapped to a point of the same color so as to allow a straightline plane drawing of each graph is the problem of colored simultaneous geometric embedding.

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U2 - 10.1007/s00453-010-9433-x

DO - 10.1007/s00453-010-9433-x

M3 - Article

VL - 60

SP - 569

EP - 592

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 3

ER -