Finding small simple cycle separators for 2-connected planar graphs
Journal of Computer and System Sciences
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Checking geometric programs or verification of geometric structures
Proceedings of the twelfth annual symposium on Computational geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
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
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Sublinear-time approximation of Euclidean minimum spanning tree
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Translating a Planar Object to Maximize Point Containment
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
Property-Preserving data reconstruction
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Space-efficient local computation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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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 (eg, 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.