### Abstract

We consider the problem of characterizing graphs with low ply number and algorithms for creating layouts of graphs with low ply number. Informally, the ply number of a straight-line drawing of a graph is defined as the maximum number of overlapping disks, where each disk is associated with a vertex and has a radius that is half the length of the longest edge incident to that vertex. We show that internally triangulated biconnected planar graphs that admit a drawing with ply number 1 can be recognized in O(n log n) time, while the problem is in general NP-hard. We also show several classes of graphs that have 1-ply drawings. We then show that binary trees, stars, and caterpillars have 2-ply drawings, while general trees have (h+1)-ply drawings, where h is the height of the tree. Finally we discuss some generalizations of the notion of a ply number.

Original language | English (US) |
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Title of host publication | IISA 2015 - 6th International Conference on Information, Intelligence, Systems and Applications |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Print) | 9781467393119 |

DOIs | |

State | Published - Jan 20 2016 |

Event | 6th International Conference on Information, Intelligence, Systems and Applications, IISA 2015 - Corfu, Greece Duration: Jul 6 2015 → Jul 8 2015 |

### Other

Other | 6th International Conference on Information, Intelligence, Systems and Applications, IISA 2015 |
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Country | Greece |

City | Corfu |

Period | 7/6/15 → 7/8/15 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science Applications
- Social Sciences (miscellaneous)
- Artificial Intelligence
- Information Systems

### Cite this

*IISA 2015 - 6th International Conference on Information, Intelligence, Systems and Applications*[7388020] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IISA.2015.7388020

**Low ply graph drawing.** / Di Giacomo, Emilio; Didimo, Walter; Hong, Seok Hee; Kaufmann, Michael; Kobourov, Stephen G; Liotta, Giuseppe; Misue, Kazuo; Symvonis, Antonios; Yen, Hsu Chun.

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

*IISA 2015 - 6th International Conference on Information, Intelligence, Systems and Applications.*, 7388020, Institute of Electrical and Electronics Engineers Inc., 6th International Conference on Information, Intelligence, Systems and Applications, IISA 2015, Corfu, Greece, 7/6/15. https://doi.org/10.1109/IISA.2015.7388020

}

TY - GEN

T1 - Low ply graph drawing

AU - Di Giacomo, Emilio

AU - Didimo, Walter

AU - Hong, Seok Hee

AU - Kaufmann, Michael

AU - Kobourov, Stephen G

AU - Liotta, Giuseppe

AU - Misue, Kazuo

AU - Symvonis, Antonios

AU - Yen, Hsu Chun

PY - 2016/1/20

Y1 - 2016/1/20

N2 - We consider the problem of characterizing graphs with low ply number and algorithms for creating layouts of graphs with low ply number. Informally, the ply number of a straight-line drawing of a graph is defined as the maximum number of overlapping disks, where each disk is associated with a vertex and has a radius that is half the length of the longest edge incident to that vertex. We show that internally triangulated biconnected planar graphs that admit a drawing with ply number 1 can be recognized in O(n log n) time, while the problem is in general NP-hard. We also show several classes of graphs that have 1-ply drawings. We then show that binary trees, stars, and caterpillars have 2-ply drawings, while general trees have (h+1)-ply drawings, where h is the height of the tree. Finally we discuss some generalizations of the notion of a ply number.

AB - We consider the problem of characterizing graphs with low ply number and algorithms for creating layouts of graphs with low ply number. Informally, the ply number of a straight-line drawing of a graph is defined as the maximum number of overlapping disks, where each disk is associated with a vertex and has a radius that is half the length of the longest edge incident to that vertex. We show that internally triangulated biconnected planar graphs that admit a drawing with ply number 1 can be recognized in O(n log n) time, while the problem is in general NP-hard. We also show several classes of graphs that have 1-ply drawings. We then show that binary trees, stars, and caterpillars have 2-ply drawings, while general trees have (h+1)-ply drawings, where h is the height of the tree. Finally we discuss some generalizations of the notion of a ply number.

UR - http://www.scopus.com/inward/record.url?scp=84963787567&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84963787567&partnerID=8YFLogxK

U2 - 10.1109/IISA.2015.7388020

DO - 10.1109/IISA.2015.7388020

M3 - Conference contribution

AN - SCOPUS:84963787567

SN - 9781467393119

BT - IISA 2015 - 6th International Conference on Information, Intelligence, Systems and Applications

PB - Institute of Electrical and Electronics Engineers Inc.

ER -