Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Algorithms for dynamic closest pair and n-body potential fields
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Data structures for mobile data
Journal of Algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Approximation algorithms
Space-efficient approximate Voronoi diagrams
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Collision detection for deforming necklaces
Proceedings of the eighteenth annual symposium on Computational geometry
Efficient maintenance and self-collision testing for Kinematic Chains
Proceedings of the eighteenth annual symposium on Computational geometry
Dense point sets have sparse Delaunay triangulations: or "…but not too nasty"
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Linear-size approximate voronoi diagrams
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate distance oracles for geometric graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
Smooth kinetic maintenance of clusters
Proceedings of the nineteenth annual symposium on Computational geometry
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Navigating nets: simple algorithms for proximity search
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal parallel all-nearest-neighbors using the well-separated pair decomposition
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Randomized and deterministic algorithms for geometric spanners of small diameter
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Distributed proximity maintenance in ad hoc mobile networks
DCOSS'05 Proceedings of the First IEEE international conference on Distributed Computing in Sensor Systems
Maintaining Nets and Net Trees under Incremental Motion
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Balls hierarchy: image segmentation by graph spanner
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Subspace self-collision culling
ACM SIGGRAPH 2010 papers
Kinetic maintenance of mobile k-centres on trees
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Approximation algorithm for the kinetic robust K-center problem
Computational Geometry: Theory and Applications
Maintaining approximate minimum steiner tree and k-center for mobile agents in a sensor network
INFOCOM'10 Proceedings of the 29th conference on Information communications
Proximity algorithms for nearly-doubling spaces
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Hierarchical Spatial Gossip for Multiresolution Representations in Sensor Networks
ACM Transactions on Sensor Networks (TOSN)
Proceedings of the twenty-seventh annual symposium on Computational geometry
The emergence of sparse spanners and greedy well-separated pair decomposition
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Energy-based self-collision culling for arbitrary mesh deformations
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
The traveling salesman problem: low-dimensionality implies a polynomial time approximation scheme
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Competitive query strategies for minimising the ply of the potential locations of moving points
Proceedings of the twenty-ninth annual symposium on Computational geometry
Output-sensitive well-separated pair decompositions for dynamic point sets
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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For a set S of points in R^d, an s-spanner is a subgraph of the complete graph with node set S such that any pair of points is connected via some path in the spanner whose total length is at most s times the Euclidean distance between the points. In this paper we propose a new sparse (1+@e)-spanner with O(n/@e^d) edges, where @e is a specified parameter. The key property of this spanner is that it can be efficiently maintained under dynamic insertion or deletion of points, as well as under continuous motion of the points in both the kinetic data structures setting and in the more realistic blackbox displacement model we introduce. Our deformable spanner succinctly encodes all proximity information in a deforming point cloud, giving us efficient kinetic algorithms for problems such as the closest pair, the near neighbors of all points, approximate nearest neighbor search (aka approximate Voronoi diagram), well-separated pair decompositions, and approximate k-centers.