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
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
Competitive algorithms for maintaining a mobile center
Mobile Networks and Applications
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Fast arbitrary splitting of deforming objects
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
Fully dynamic geometric spanners
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Improved algorithms for fully dynamic geometric spanners and geometric routing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The Kinetic Facility Location Problem
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
An Optimal Dynamic Spanner for Doubling Metric Spaces
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Localized Spanner Construction for Ad Hoc Networks with Variable Transmission Range
ADHOC-NOW '08 Proceedings of the 7th international conference on Ad-hoc, Mobile and Wireless Networks
Glance: A lightweight querying service for wireless sensor networks
Theoretical Computer Science
Fault-tolerant spanners for general graphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Splitting meshless deforming objects with explicit surface tracking
Graphical Models
A dynamic bounding volume hierarchy for generalized collision detection
Computers and Graphics
Efficient yarn-based cloth with adaptive contact linearization
ACM SIGGRAPH 2010 papers
Fault Tolerant Spanners for General Graphs
SIAM Journal on Computing
Kinetic convex hulls and delaunay triangulations in the black-box model
Proceedings of the twenty-seventh annual symposium on Computational geometry
GLANCE: a lightweight querying service for wireless sensor networks
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Distance-Sensitive information brokerage in sensor networks
DCOSS'06 Proceedings of the Second IEEE international conference on Distributed Computing in Sensor Systems
Distributed proximity maintenance in ad hoc mobile networks
DCOSS'05 Proceedings of the First IEEE international conference on Distributed Computing in Sensor Systems
Fast, precise and dynamic distance queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Linear-size approximations to the vietoris-rips filtration
Proceedings of the twenty-eighth annual symposium on Computational geometry
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Kinetic 2-centers in the black-box model
Proceedings of the twenty-ninth annual symposium on Computational geometry
New doubling spanners: better and simpler
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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For a set S of points in ℝ3, an s-spanner is a graph on 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+ε)-spanner with O(n/εd) edges, where ε is a specified parameter. The key property of this spanner is that it can be efficiently maintained under dynamic insertion or deletion ofpoints, 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 decomposition, and approximate k-centers.