Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
The visibility skeleton: a powerful and efficient multi-purpose global visibility tool
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
A new algorithm for computing shortest paths in weighted planar subdivisions (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximating weighted shortest paths on polyhedral surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
The 3D visibility complex: a new approach to the problems of accurate visibility
Proceedings of the eurographics workshop on Rendering techniques '96
Computing the optimal bridge between two convex polygons
Information Processing Letters
Optimizing the sum of linear fractional functions and applications
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Parallel Optimal Weighted Links
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
An epsilon-Approximation for Weighted Shortest Paths on Polyhedral Surfaces
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
On geometric optimization problems
On geometric optimization problems
1-link shortest paths in weighted regions
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
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
Line facility location in weighted regions
Journal of Combinatorial Optimization
k-link shortest paths in weighted subdivisions
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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In this paper, we present improved algorithms for computing an optimal link among weighted regions in the 2-dimensional (2-D) space. The weighted regions optimal link problem arises in several areas, such as geographic information systems (GIS), radiation therapy, geological exploration, environmental engineering and military applications. Our results are based on a (more general) theorem that characterizes a class of functions for which optimal solutions arise on the boundary of the feasible domain. A direct consequence of this theorem is that an optimal link goes through a vertex of the weighted subdivision. We also consider extensions and present results for the 3-D case. Our results imply significantly faster algorithms for solving the 3-D problem.