### Abstract

Set membership of points in the plane can be visualized by connecting corresponding points via graphical features, like paths, trees, polygons, ellipses. In this paper we study the bus embeddability problem (BEP): given a set of colored points we ask whether there exists a planar realization with one horizontal straight-line segment per color, called bus, such that all points with the same color are connected with vertical line segments to their bus. We present an ILP and an FPT algorithm for the general problem. For restricted versions of this problem, such as when the relative order of buses is predefined, or when a bus must be placed above all its points, we provide efficient algorithms. We show that another restricted version of the problem can be solved using 2-stack pushall sorting. On the negative side we prove the NP-completeness of a special case of BEP.

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

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

Publisher | Springer Verlag |

Pages | 395-408 |

Number of pages | 14 |

Volume | 9411 |

ISBN (Print) | 9783319272603 |

DOIs | |

State | Published - 2015 |

Event | 23rd International Symposium on Graph Drawing and Network Visualization, GD 2015 - Los Angeles, United States Duration: Sep 24 2015 → Sep 26 2015 |

### Publication series

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

Volume | 9411 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 23rd International Symposium on Graph Drawing and Network Visualization, GD 2015 |
---|---|

Country | United States |

City | Los Angeles |

Period | 9/24/15 → 9/26/15 |

### Fingerprint

### 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. 9411, pp. 395-408). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9411). Springer Verlag. https://doi.org/10.1007/978-3-319-27261-0_33

**On embeddability of buses in point sets.** / Bruckdorfer, Till; Kaufmann, Michael; Kobourov, Stephen G; Pupyrev, Sergey.

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. 9411, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9411, Springer Verlag, pp. 395-408, 23rd International Symposium on Graph Drawing and Network Visualization, GD 2015, Los Angeles, United States, 9/24/15. https://doi.org/10.1007/978-3-319-27261-0_33

}

TY - GEN

T1 - On embeddability of buses in point sets

AU - Bruckdorfer, Till

AU - Kaufmann, Michael

AU - Kobourov, Stephen G

AU - Pupyrev, Sergey

PY - 2015

Y1 - 2015

N2 - Set membership of points in the plane can be visualized by connecting corresponding points via graphical features, like paths, trees, polygons, ellipses. In this paper we study the bus embeddability problem (BEP): given a set of colored points we ask whether there exists a planar realization with one horizontal straight-line segment per color, called bus, such that all points with the same color are connected with vertical line segments to their bus. We present an ILP and an FPT algorithm for the general problem. For restricted versions of this problem, such as when the relative order of buses is predefined, or when a bus must be placed above all its points, we provide efficient algorithms. We show that another restricted version of the problem can be solved using 2-stack pushall sorting. On the negative side we prove the NP-completeness of a special case of BEP.

AB - Set membership of points in the plane can be visualized by connecting corresponding points via graphical features, like paths, trees, polygons, ellipses. In this paper we study the bus embeddability problem (BEP): given a set of colored points we ask whether there exists a planar realization with one horizontal straight-line segment per color, called bus, such that all points with the same color are connected with vertical line segments to their bus. We present an ILP and an FPT algorithm for the general problem. For restricted versions of this problem, such as when the relative order of buses is predefined, or when a bus must be placed above all its points, we provide efficient algorithms. We show that another restricted version of the problem can be solved using 2-stack pushall sorting. On the negative side we prove the NP-completeness of a special case of BEP.

UR - http://www.scopus.com/inward/record.url?scp=84951974834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951974834&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-27261-0_33

DO - 10.1007/978-3-319-27261-0_33

M3 - Conference contribution

SN - 9783319272603

VL - 9411

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

SP - 395

EP - 408

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

PB - Springer Verlag

ER -