Randomized multidimensional search trees (extended abstract): dynamic sampling
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Dynamic maintenance of geometric structures made easy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Applications of random sampling to on-line algorithms in computational geometry
Discrete & Computational Geometry
Four results on randomized incremental constructions
Computational Geometry: Theory and Applications
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
Generating well-shaped Delaunay meshed in 3D
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A virtual node algorithm for changing mesh topology during simulation
ACM SIGGRAPH 2004 Papers
A time-optimal delaunay refinement algorithm in two dimensions
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Self-adjusting computation
An experimental analysis of self-adjusting computation
Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
Dynamic mesh refinement
A cost semantics for self-adjusting computation
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Interactive simulation of surgical needle insertion and steering
ACM SIGGRAPH 2009 papers
Traceable data types for self-adjusting computation
PLDI '10 Proceedings of the 2010 ACM SIGPLAN conference on Programming language design and implementation
Parallelism in dynamic well-spaced point sets
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Proceedings of the twenty-seventh annual symposium on Computational geometry
Implicit self-adjusting computation for purely functional programs
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
Proceedings of the 2011 ACM international conference on Object oriented programming systems languages and applications
Type-directed automatic incrementalization
Proceedings of the 33rd ACM SIGPLAN conference on Programming Language Design and Implementation
Non-monotonic self-adjusting computation
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
Dynamic well-spaced point sets
Computational Geometry: Theory and Applications
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In a well-spaced point set, when there is a bounding hypercube, the Voronoi cells all have bounded aspect ratio, i.e., the distance from the Voronoi site to the farthest point in the Voronoi cell divided by the distance to the nearest neighbor in the set is bounded by a small constant. Well-spaced point sets satisfy some important geometric properties and yield quality Voronoi or simplicial meshes that can be important in scientific computations. In this paper, we consider the dynamic well-spaced point sets problem, which requires computing the well-spaced superset of a dynamically changing input set, e.g., as input points are inserted or deleted. We present a dynamic algorithm that allows inserting/deleting points into/from the input in worst-case O(log Δ) time, where Δ is the geometric spread, a natural measure that is bounded by O(log n) when input points are represented by log-size words. We show that the runtime of the dynamic update algorithm is optimal in the worst case. Our algorithm generates size-optimal outputs: the resulting output sets are never more than a constant factor larger than the minimum size necessary. A preliminary implementation indicates that the algorithm is indeed fast in practice. To the best of our knowledge, this is the first time- and size-optimal dynamic algorithm for well-spaced point sets.