The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
Optimizing the sum of linear fractional functions
Recent advances in global optimization
A new algorithm for computing shortest paths in weighted planar subdivisions (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Improved Optimal Weighted Links Algorithms
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Determining approximate shortest paths on weighted polyhedral surfaces
Journal of the ACM (JACM)
Computing a shortest k-link path in a polygon
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Approximating minimum-cost polygonal paths of bounded number of links in weighted subdivisions
Proceedings of the twenty-second annual symposium on Computational geometry
Finding optimal weighted bridges with applications
Proceedings of the 44th annual Southeast regional conference
Parallel Optimal Weighted Links
Transactions on Computational Science III
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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 ε0. 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.