Tail estimates for the space complexity of randomized incremental algorithms
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Ray shooting in convex polytopes
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On randomization in sequential and distributed algorithms
ACM Computing Surveys (CSUR)
ACM Computing Surveys (CSUR)
Average case analysis of dynamic geometric optimization
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Dynamic planar convex hull operations in near-logarithmic amortized time
Journal of the ACM (JACM)
Simple randomized algorithms for closest pair problems
Nordic Journal of Computing
Dynamic Planar Convex Hull with Optimal Query Time
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Dynamic Planar Convex Hull Operations in Near-Logarithmic Amortized Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Dynamizing static algorithms, with applications to dynamic trees and history independence
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Markov incremental constructions
Proceedings of the twenty-fourth annual symposium on Computational geometry
A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries
Journal of the ACM (JACM)
Dynamic well-spaced point sets
Proceedings of the twenty-sixth annual symposium on Computational geometry
Parallelism in dynamic well-spaced point sets
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
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The problem of dynamically maintaining geometric structures is considered. A technique is proposed that uses randomized incremental algorithms which are augmented to allow deletions of objects. A model for distributions on the possible input sequences of insertions and deletions is developed and analyzed using R. Seidel's backwards analysis. It is further shown how to apply this to maintain Voronoi diagrams, convex hulls, and planar subdivisions. A strikingly simple algorithm for the maintenance of convex hulls in any dimension is given. The expected running time is determined.