Checking geometric programs or verification of geometric structures
Proceedings of the twelfth annual symposium on Computational geometry
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Surface Approximation and Geometric Partitions
SIAM Journal on Computing
Sublinear time algorithms for metric space problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
An efficient algorithm for terrain simplification
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Sublinear time approximate clustering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Sublinear-time approximation of Euclidean minimum spanning tree
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Property Testing in Computational Geometry
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Property Testing with Geometric Queries
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Near-Linear Time Approximation Algorithms for Curve Simplification
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Sublinear geometric algorithms
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A Sublinear Time Approximation Scheme for Clustering in Metric Spaces
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Estimating the weight of metric minimum spanning trees in sublinear-time
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
Noise Tolerance of Expanders and Sublinear Expander Reconstruction
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Testability and repair of hereditary hypergraph properties
Random Structures & Algorithms
Lower bounds for local monotonicity reconstruction from transitive-closure spanners
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Estimating the Longest Increasing Sequence in Polylogarithmic Time
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Property-Preserving data reconstruction
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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We investigate a new class of geometric problems based on the idea of online error correction. Suppose one is given access to a large geometric dataset though a query mechanism; for example, the dataset could be a terrain and a query might ask for the coordinates of a particular vertex or for the edges incident to it. Suppose, in addition, that the dataset satisfies some known structural property P (for example, monotonicity or convexity) but that, because of errors and noise, the queries occasionally provide answers that violate P. Can one design a filter that modifies the query's answers so that (i) the output satisfies P; (ii) the amount of data modification is minimized? We provide upper and lower bounds on the complexity of online reconstruction for convexity in 2D and 3D.