### Abstract

Let A be a plane region which is bounded by an outer rectangle and an inner one and has r rectangular obstacles inside the region. Let k terminal pairs lie on the outer and inner rectangular boundaries. This paper presents an efficient algorithm which finds k “non-crossing” rectilinear paths in the plane region A, each connecting a terminal pair without passing through any obstacles, whose total length is minimum. Non-crossing paths may share common points or line segments but do not cross each other in the plane. The algorithm runs in time O(n log n) where n=r+k.

Original language | English |
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Title of host publication | Algorithms and Computation - 4th International Symposium, ISAAC 1993, Proceedings |

Editors | Kam Wing Ng, Prabhakar Raghavan, N.V. Balasubramanian, Francis Y.L. Chin |

Publisher | Springer Verlag |

Pages | 98-107 |

Number of pages | 10 |

ISBN (Print) | 9783540575689 |

DOIs | |

Publication status | Published - 1993 |

Event | 4th International Symposium on Algorithms and Computation, ISAAC 1993 - Hong Kong, China Duration: 1993 Dec 15 → 1993 Dec 17 |

### 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 | 762 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 4th International Symposium on Algorithms and Computation, ISAAC 1993 |
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Country | China |

City | Hong Kong |

Period | 93/12/15 → 93/12/17 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Takahashi, J. Y., Suzuki, H., & Nishizeki, T. (1993). Finding shortest non-crossing rectilinear paths in plane regions. In K. W. Ng, P. Raghavan, N. V. Balasubramanian, & F. Y. L. Chin (Eds.),

*Algorithms and Computation - 4th International Symposium, ISAAC 1993, Proceedings*(pp. 98-107). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 762 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-57568-5_239