### Abstract

The method to construct an arrangement of n lines having a monotone path was presented. It was observed that k parallel horizontal lines and k parallel vertical lines uses n lines and has a length n=2k. It was found that a path is monotone in direction (a,b) if its sequence of vertices is monotone when projected orthogonally along the line with equation ay-bx=0.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Pages | 124-128 |

Number of pages | 5 |

State | Published - 2003 |

Event | Nineteenth Annual Symposium on Computational Geometry - san Diego, CA, United States Duration: Jun 8 2003 → Jun 10 2003 |

### Other

Other | Nineteenth Annual Symposium on Computational Geometry |
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Country | United States |

City | san Diego, CA |

Period | 6/8/03 → 6/10/03 |

### Keywords

- Discrete Line Arrangements
- Monotone Paths

### ASJC Scopus subject areas

- Software
- Geometry and Topology
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

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## Cite this

Balogh, J., Regev, O., Smyth, C., Steiger, W., & Szegedy, M. (2003). Long monotone paths in line arrangements. In

*Proceedings of the Annual Symposium on Computational Geometry*(pp. 124-128)