Controlled perturbation for arrangements of polyhedral surfaces with application to swept volumes
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
I/O-efficient dynamic point location in monotone planar subdivisions
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
I/O-efficient dynamic planar point location (extended abstract)
Proceedings of the sixteenth annual symposium on Computational geometry
Java applets for the dynamic visualization of Voronoi diagrams
Computer Science in Perspective
I/O-efficient dynamic planar point location
Computational Geometry: Theory and Applications
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
External memory planar point location with logarithmic updates
Proceedings of the twenty-fourth annual symposium on Computational geometry
Relative Convex Hulls in Semi-dynamic Subdivisions
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions
ACM Transactions on Algorithms (TALG)
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We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map $\cal M$ with $n$ vertices and apply it to the development of a unified dynamic data structure that supports point-location, ray-shooting, and shortest-path queries in $\cal M$. The space requirement is $O(n\log n)$. Point-location queries take time $O(\log n)$. Ray-shooting and shortest-path queries take time $O(\log^3 n)$ (plus $O(k)$ time if the $k$ edges of the shortest path are reported in addition to its length). Updates consist of insertions and deletions of vertices and edges, and take $O(\log^3 n)$ time (amortized for vertex updates). This is the first polylog-time dynamic data structure for shortest-path and ray-shooting queries. It is also the first dynamic point-location data structure for connected planar maps that achieves optimal query time.