A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Discrete Applied Mathematics
Proximity problems on line segments spanned by points
Computational Geometry: Theory and Applications
An O(nlogn) algorithm for the all-farthest-segments problem for a planar set of points
Information Processing Letters
Approximation Algorithms for Finding a Minimum Perimeter Polygon Intersecting a Set of Line Segments
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Farthest segments and extremal triangles spanned by points in R3
Information Processing Letters
Farthest-polygon Voronoi diagrams
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Higher order Voronoi diagrams of segments for VLSI critical area extraction
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Discrete construction of order-k voronoi diagram
ICICA'10 Proceedings of the First international conference on Information computing and applications
Farthest-polygon Voronoi diagrams
Computational Geometry: Theory and Applications
Improved algorithms for farthest colored voronoi diagram of segments
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Discrete construction of power network voronoi diagram
ICICA'11 Proceedings of the Second international conference on Information Computing and Applications
All-maximum and all-minimum problems under some measures
Journal of Discrete Algorithms
Improved algorithms for the farthest colored Voronoi diagram of segments
Theoretical Computer Science
On the complexity of higher order abstract voronoi diagrams
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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The farthest line segment Voronoi diagram shows properties different from both the closest-segment Voronoi diagram and the farthest-point Voronoi diagram. Surprisingly, this structure did not receive attention in the computational geometry literature. We analyze its combinatorial and topological properties and outline an O(n log n) time construction algorithm that is easy to implement. No restrictions are placed upon the n input line segments; they are allowed to touch or cross.