### Abstract

The computation of shortest paths, distances and feature relationships is a key problem in many applications. In finding shortest distances or paths one often must respect features of the domain. For example, in medical applications such as radiation therapy, the features may include tissue density, risk to radiation exposure, etc. In computing an optimal treatment plan, one can think of these features as weights that effect a cost per unit travel distance function. In this model, the cost of travelling through 2 cm of dense bone might be more than the cost of travelling through 5 cm of very soft tissue. One possible way to model such problems is as shortest path problems in weighted regions. A special case of shortest path problems in weighted regions is that of computing an optimal weighted bridge between two regions. In this version, we are given two disjoint convex polygons P and Q in a weighted subdivision R. A weighted bridge. B_{w}, is a path from a point p ∈ P to a point q ∈ Q that connects P and Q such that the sum of the weighted length of B_{w} and the maximum weighted distance from any point in P to p and from any point in Q to q is minimized. The goal is to compute an optimal weighted bridge between P and Q. In this paper, we describe 2-factor and (1 + ε)-factor approximation schemes for finding optimal 1-link weighted bridges between a pair of convex polygons. We also describe how these techniques can be extended to k-link weighted bridges and weighted bridges where the number of links is not restricted.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the Annual Southeast Conference |

Pages | 12-17 |

Number of pages | 6 |

Volume | 2006 |

DOIs | |

State | Published - 2006 |

Externally published | Yes |

Event | 44th Annual ACM Southeast Conference, ACMSE 2006 - Melbourne, FL, United States Duration: Mar 10 2006 → Mar 12 2006 |

### Other

Other | 44th Annual ACM Southeast Conference, ACMSE 2006 |
---|---|

Country | United States |

City | Melbourne, FL |

Period | 3/10/06 → 3/12/06 |

### Fingerprint

### Keywords

- Optimal bridges
- Path planning
- Weighted regions

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the Annual Southeast Conference*(Vol. 2006, pp. 12-17) https://doi.org/10.1145/1185448.1185452

**Finding optimal weighted bridges with applications.** / Daescu, Ovidiu; Palmer, James D.

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

*Proceedings of the Annual Southeast Conference.*vol. 2006, pp. 12-17, 44th Annual ACM Southeast Conference, ACMSE 2006, Melbourne, FL, United States, 3/10/06. https://doi.org/10.1145/1185448.1185452

}

TY - GEN

T1 - Finding optimal weighted bridges with applications

AU - Daescu, Ovidiu

AU - Palmer, James D

PY - 2006

Y1 - 2006

N2 - The computation of shortest paths, distances and feature relationships is a key problem in many applications. In finding shortest distances or paths one often must respect features of the domain. For example, in medical applications such as radiation therapy, the features may include tissue density, risk to radiation exposure, etc. In computing an optimal treatment plan, one can think of these features as weights that effect a cost per unit travel distance function. In this model, the cost of travelling through 2 cm of dense bone might be more than the cost of travelling through 5 cm of very soft tissue. One possible way to model such problems is as shortest path problems in weighted regions. A special case of shortest path problems in weighted regions is that of computing an optimal weighted bridge between two regions. In this version, we are given two disjoint convex polygons P and Q in a weighted subdivision R. A weighted bridge. Bw, is a path from a point p ∈ P to a point q ∈ Q that connects P and Q such that the sum of the weighted length of Bw and the maximum weighted distance from any point in P to p and from any point in Q to q is minimized. The goal is to compute an optimal weighted bridge between P and Q. In this paper, we describe 2-factor and (1 + ε)-factor approximation schemes for finding optimal 1-link weighted bridges between a pair of convex polygons. We also describe how these techniques can be extended to k-link weighted bridges and weighted bridges where the number of links is not restricted.

AB - The computation of shortest paths, distances and feature relationships is a key problem in many applications. In finding shortest distances or paths one often must respect features of the domain. For example, in medical applications such as radiation therapy, the features may include tissue density, risk to radiation exposure, etc. In computing an optimal treatment plan, one can think of these features as weights that effect a cost per unit travel distance function. In this model, the cost of travelling through 2 cm of dense bone might be more than the cost of travelling through 5 cm of very soft tissue. One possible way to model such problems is as shortest path problems in weighted regions. A special case of shortest path problems in weighted regions is that of computing an optimal weighted bridge between two regions. In this version, we are given two disjoint convex polygons P and Q in a weighted subdivision R. A weighted bridge. Bw, is a path from a point p ∈ P to a point q ∈ Q that connects P and Q such that the sum of the weighted length of Bw and the maximum weighted distance from any point in P to p and from any point in Q to q is minimized. The goal is to compute an optimal weighted bridge between P and Q. In this paper, we describe 2-factor and (1 + ε)-factor approximation schemes for finding optimal 1-link weighted bridges between a pair of convex polygons. We also describe how these techniques can be extended to k-link weighted bridges and weighted bridges where the number of links is not restricted.

KW - Optimal bridges

KW - Path planning

KW - Weighted regions

UR - http://www.scopus.com/inward/record.url?scp=34248395505&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34248395505&partnerID=8YFLogxK

U2 - 10.1145/1185448.1185452

DO - 10.1145/1185448.1185452

M3 - Conference contribution

AN - SCOPUS:34248395505

SN - 1595933158

SN - 9781595933157

VL - 2006

SP - 12

EP - 17

BT - Proceedings of the Annual Southeast Conference

ER -