### Abstract

We study compact straight-line embeddings of trees. We show that perfect binary trees can be embedded optimally: a tree with n nodes can be drawn on a √n by √n grid. We also show that testing whether a given binary tree has an upward embedding with a given combinatorial embedding in a given grid is NP-hard.

Original language | English |
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Title of host publication | Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings |

Publisher | Springer Verlag Heidelberg |

Pages | 361-367 |

Number of pages | 7 |

ISBN (Print) | 9783030044138 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

Event | 26th International Symposium on Graph Drawing and Network Visualization, GD 2018 - Barcelona, Spain Duration: 26 Sep 2018 → 28 Sep 2018 |

### 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 | 11282 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 26th International Symposium on Graph Drawing and Network Visualization, GD 2018 |
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Country | Spain |

City | Barcelona |

Period | 26/09/18 → 28/09/18 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings*(pp. 361-367). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11282 LNCS). Springer Verlag Heidelberg. https://doi.org/10.1007/978-3-030-04414-5_26

**How to fit a tree in a box.** / Akitaya, Hugo A.; Löffler, Maarten; Parada, Irene.

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

*Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11282 LNCS, Springer Verlag Heidelberg, pp. 361-367, 26th International Symposium on Graph Drawing and Network Visualization, GD 2018, Barcelona, Spain, 26/09/18. https://doi.org/10.1007/978-3-030-04414-5_26

}

TY - GEN

T1 - How to fit a tree in a box

AU - Akitaya, Hugo A.

AU - Löffler, Maarten

AU - Parada, Irene

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We study compact straight-line embeddings of trees. We show that perfect binary trees can be embedded optimally: a tree with n nodes can be drawn on a √n by √n grid. We also show that testing whether a given binary tree has an upward embedding with a given combinatorial embedding in a given grid is NP-hard.

AB - We study compact straight-line embeddings of trees. We show that perfect binary trees can be embedded optimally: a tree with n nodes can be drawn on a √n by √n grid. We also show that testing whether a given binary tree has an upward embedding with a given combinatorial embedding in a given grid is NP-hard.

UR - http://www.scopus.com/inward/record.url?scp=85059101441&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-04414-5_26

DO - 10.1007/978-3-030-04414-5_26

M3 - Conference contribution

SN - 9783030044138

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

SP - 361

EP - 367

BT - Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings

PB - Springer Verlag Heidelberg

ER -