### Abstract

We study the shortest path problem in weighted polygonal subdivisions of the plane, with the additional constraint of an upper bound, k, on the number of links (segments) in the path. We prove structural properties of optimal paths and utilize these results to obtain approximation algorithms that yield a path having O(k) links and weighted length at most (1 + ε) times the weighted length of an optimal k-link path, for any fixed ε > 0. Some of our results make use of a new solution for the 1-link case, based on computing optimal solutions for a special sum-of-fractionals (SOF) problem. We have implemented a system, based on the CORE library, for computing optimal 1-link paths; we experimentally compare our new solution with a previous method for 1-link optimal paths based on a prune-and-search scheme.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science |

Editors | F. Dehne, A. Lopez-Ortiz, J.-R. Sack |

Pages | 325-337 |

Number of pages | 13 |

Volume | 3608 |

State | Published - 2005 |

Externally published | Yes |

Event | 9th International Workshop on Algorithms and Data Structures, WADS 2005 - Waterloo, Canada Duration: Aug 15 2005 → Aug 17 2005 |

### Other

Other | 9th International Workshop on Algorithms and Data Structures, WADS 2005 |
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Country | Canada |

City | Waterloo |

Period | 8/15/05 → 8/17/05 |

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### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

*Lecture Notes in Computer Science*(Vol. 3608, pp. 325-337)