### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

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

**k-Link shortest paths in weighted subdivisions.** / Daescu, Ovidiu; Mitchell, Joseph S B; Ntafos, Simeon; Palmer, James D; Yap, Chee K.

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

*Lecture Notes in Computer Science.*vol. 3608, pp. 325-337, 9th International Workshop on Algorithms and Data Structures, WADS 2005, Waterloo, Canada, 8/15/05.

}

TY - GEN

T1 - k-Link shortest paths in weighted subdivisions

AU - Daescu, Ovidiu

AU - Mitchell, Joseph S B

AU - Ntafos, Simeon

AU - Palmer, James D

AU - Yap, Chee K.

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=26844496069&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26844496069&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:26844496069

VL - 3608

SP - 325

EP - 337

BT - Lecture Notes in Computer Science

A2 - Dehne, F.

A2 - Lopez-Ortiz, A.

A2 - Sack, J.-R.

ER -