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Inner and outer j-radii of convex bodies in finite-dimensional normed spaces
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A Subexponential Algorithm for Abstract Optimization Problems
SIAM Journal on Computing
On linear-time deterministic algorithms for optimization problems in fixed dimension
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Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Efficient approximation and optimization algorithms for computational metrology
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Data structures for mobile data
Journal of Algorithms
Indexing the positions of continuously moving objects
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithms for a Minimum Volume Enclosing Simplex in Three Dimensions
SIAM Journal on Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
STAR-Tree: An Efficient Self-Adjusting Index for Moving Objects
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Approximation Algorithms for k-Line Center
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Journal of Computer and System Sciences - Special issue on PODS 2000
Multi-dimensional regression analysis of time-series data streams
VLDB '02 Proceedings of the 28th international conference on Very Large Data Bases
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VLDB '02 Proceedings of the 28th international conference on Very Large Data Bases
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Practical methods for shape fitting and kinetic data structures using core sets
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
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STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Adaptive sampling for geometric problems over data streams
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Subgradient and sampling algorithms for l1 regression
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Robust shape fitting via peeling and grating coresets
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Analysis of incomplete data and an intrinsic-dimension Helly theorem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On k-Median clustering in high dimensions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A fast k-means implementation using coresets
Proceedings of the twenty-second annual symposium on Computational geometry
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Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets
Computational Geometry: Theory and Applications
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Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
Deterministic sampling and range counting in geometric data streams
ACM Transactions on Algorithms (TALG)
A space-optimal data-stream algorithm for coresets in the plane
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Embeddings of surfaces, curves, and moving points in euclidean space
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Out-of-order event processing in kinetic data structures
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Adaptive sampling for geometric problems over data streams
Computational Geometry: Theory and Applications
Sampling algorithms and coresets for ℓp regression
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Proceedings of the twenty-fourth annual symposium on Computational geometry
Summarizing spatial data streams using ClusterHulls
Journal of Experimental Algorithmics (JEA)
Simplified Planar Coresets for Data Streams
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
The Kinetic Facility Location Problem
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Single facility collection depots location problem in the plane
Computational Geometry: Theory and Applications
Proceedings of the forty-first annual ACM symposium on Theory of computing
Coresets for polytope distance
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Answering linear optimization queries with an approximate stream index
Knowledge and Information Systems
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Computational Geometry: Theory and Applications
Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets
Computational Geometry: Theory and Applications
Extremal point queries with lines and line segments and related problems
Computational Geometry: Theory and Applications
Streamed learning: one-pass SVMs
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Hausdorff distance under translation for points and balls
ACM Transactions on Algorithms (TALG)
Coresets and sketches for high dimensional subspace approximation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Streaming algorithms for extent problems in high dimensions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Approximating parameterized convex optimization problems
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Optimal consensus set for annulus fitting
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Fast oriented bounding box optimization on the rotation group SO(3,ℝ)
ACM Transactions on Graphics (TOG)
Streaming and dynamic algorithms for minimum enclosing balls in high dimensions
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Horoball hulls and extents in positive definite space
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Width of points in the streaming model
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Lower bounds for number-in-hand multiparty communication complexity, made easy
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A near-linear algorithm for projective clustering integer points
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Stacking and bundling two convex polygons
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Geometric optimization problems over sliding windows
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Adaptive spatial partitioning for multidimensional data streams
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Streaming algorithms for geometric problems
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
From high definition image to low space optimization
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
StreamKM++: A clustering algorithm for data streams
Journal of Experimental Algorithmics (JEA)
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Processing a large number of continuous preference top-k queries
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
Two-Dimensional range diameter queries
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
An optimal O(nlogn) algorithm for finding an enclosing planar rectilinear annulus of minimum width
Operations Research Letters
Scandinavian thins on top of cake: on the smallest one-size-fits-all box
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
Approximating parameterized convex optimization problems
ACM Transactions on Algorithms (TALG)
A linear time approximation scheme for computing geometric maximum k-star
Journal of Global Optimization
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Net and prune: a linear time algorithm for euclidean distance problems
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Learning Big (Image) Data via Coresets for Dictionaries
Journal of Mathematical Imaging and Vision
Data stream clustering: A survey
ACM Computing Surveys (CSUR)
Streaming with minimum space: An algorithm for covering by two congruent balls
Theoretical Computer Science
Streaming and dynamic algorithms for minimum enclosing balls in high dimensions
Computational Geometry: Theory and Applications
Data structures for range-aggregate extent queries
Computational Geometry: Theory and Applications
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We present a general technique for approximating various descriptors of the extent of a set P of n points in Rd when the dimension d is an arbitrary fixed constant. For a given extent measure μ and a parameter ϵ 0, it computes in time O(n + 1/ϵO(1)) a subset Q ⊆ P of size 1/ϵO(1), with the property that (1 − ϵ)μ(P) ≤ μ(Q) ≤ μ(P). The specific applications of our technique include ϵ-approximation algorithms for (i) computing diameter, width, and smallest bounding box, ball, and cylinder of P, (ii) maintaining all the previous measures for a set of moving points, and (iii) fitting spheres and cylinders through a point set P. Our algorithms are considerably simpler, and faster in many cases, than previously known algorithms.