### Abstract

Let G be an undirected plane graph with nonnegative edge length, and let k terminal pairs lie on two specified face boundaries. This paper presents an algorithm for finding k "noncrossing paths" in G, each connecting a terminal pair, and whose total length is minimum. Noncrossing paths may share common vertices or edges but do not cross each other in the plane. The algorithm runs in time O(n log n) where n is the number of vertices in G and k is an arbitrary integer.

Original language | English |
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Pages (from-to) | 339-357 |

Number of pages | 19 |

Journal | Algorithmica (New York) |

Volume | 16 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1996 Sep |

Externally published | Yes |

### Keywords

- Noncrossing paths
- Plane graphs
- Shortest path
- Single-layer routing
- VLSI

### ASJC Scopus subject areas

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

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## Cite this

Takahashi, J. Y., Suzuki, H., & Nishizeki, T. (1996). Shortest Noncrossing Paths in Plane Graphs.

*Algorithmica (New York)*,*16*(3), 339-357. https://doi.org/10.1007/bf01955681