Computational geometry: an introduction
Computational geometry: an introduction
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Randomized multidimensional search trees: lazy balancing and dynamic shuffling (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Dynamic maintenance of geometric structures made easy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Off-line maintenance of planar configurations
Journal of Algorithms
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Reporting Red-Blue Intersections between Two Sets of Connected Line Segments
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Dynamic Planar Convex Hull Operations in Near-Logarithmic Amortized Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Taking a Walk in a Planar Arrangement
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Reporting Intersecting Pairs of Polytopes in Two and Three Dimensions
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Three problems about dynamic convex hulls
Proceedings of the twenty-seventh annual symposium on Computational geometry
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The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n ċ log log log n) time, point deletions in amortized O(log n ċ log log n) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requires O(n) space. Applications of the new dynamic convex hull data structure are improved deterministic algorithms for the k-level problem and the redblue segment intersection problem where all red and all blue segments are connected.