TY - GEN

T1 - Finding optimal weighted bridges with applications

AU - Daescu, Ovidiu

AU - Palmer, James D.

PY - 2006/12/1

Y1 - 2006/12/1

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

T3 - Proceedings of the Annual Southeast Conference

SP - 12

EP - 17

BT - Proceedings of the 44th ACM Southeast Conference, ACMSE 2006

T2 - 44th Annual ACM Southeast Conference, ACMSE 2006

Y2 - 10 March 2006 through 12 March 2006

ER -