Partition trees for triangle counting and other range searching problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Introduction to algorithms
On learning a union of half spaces
Journal of Complexity
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Quasi-optimal range searching in spaces of finite VC-dimension
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Training a 3-node neural network is NP-complete
COLT '88 Proceedings of the first annual workshop on Computational learning theory
How to net a lot with little: small &egr;-nets for disks and halfspaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Cutting hyperplane arrangements
Discrete & Computational Geometry
An optimal convex hull algorithm and new results on cuttings (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Discrepancy and &egr; approximations for bounded VC-dimension
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Separation and approximation of polyhedral objects
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Range searching with efficient hierarchical cuttings
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Almost tight bounds for &egr;-nets
Discrete & Computational Geometry
Reporting points in halfspaces
Computational Geometry: Theory and Applications
Geometric partitioning made easier, even in parallel
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Decision trees for geometric models
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
On the hardness of approximating minimization problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Improved bounds on weak &egr;-nets for convex sets
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient NC algorithms for set cover with applications to learning and geometry
Proceedings of the 30th IEEE symposium on Foundations of computer science
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
On linear-time deterministic algorithms for optimization problems in fixed dimension
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Algorithms for Polytope Covering and Approximation
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Approximation schemes in computational geometry
Approximation schemes in computational geometry
GASP: a system to facilitate animating geometric algorithms
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Almost optimal polyhedral separators
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Noise-tolerant distribution-free learning of general geometric concepts
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Noise-tolerant distribution-free learning of general geometric concepts
Journal of the ACM (JACM)
Randomized rounding without solving the linear program
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Circular separability of polygon
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Fixed-dimensional parallel linear programming via relative &egr;-approximations
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Data collection for the Sloan Digital Sky Survey—a network-flow heuristic
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Selecting forwarding neighbors in wireless Ad Hoc networks
DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
On point covers of c-oriented polygons
Theoretical Computer Science
Learning fixed-dimension linear thresholds from fragmented data
Information and Computation
Controlled Topology Simplification
IEEE Transactions on Visualization and Computer Graphics
On Rectangular Partitionings in Two Dimensions: Algorithms, Complexity, and Applications
ICDT '99 Proceedings of the 7th International Conference on Database Theory
Automatic generation of triangular irregular networks using greedy cuts
VIS '95 Proceedings of the 6th conference on Visualization '95
Selecting forwarding neighbors in wireless ad hoc networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
Automatic Subspace Clustering of High Dimensional Data
Data Mining and Knowledge Discovery
Efficient data dissemination using locale covers
Pervasive and Mobile Computing
Providing location privacy in assisted living environments
Proceedings of the 1st international conference on PErvasive Technologies Related to Assistive Environments
Relaxation in text search using taxonomies
Proceedings of the VLDB Endowment
Scheduling forwarding nodes for two-hop neighborhoods broadcast in wireless ad hoc networks
ACOS'06 Proceedings of the 5th WSEAS international conference on Applied computer science
CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
On dependent randomized rounding algorithms
Operations Research Letters
A pseudopolynomial time O(log n)-approximation algorithm for art gallery problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Parallel data mining revisited. better, not faster
IDA'12 Proceedings of the 11th international conference on Advances in Intelligent Data Analysis
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We give a deterministic polynomial time method for finding a set cover in a set system (X,R) of VC-dimension d such that the size of our cover is at most a factor of O(dlog(dc)) from the optimal size, c. For constant VC-dimension set systems, which are common in computational geometry, our method gives an O(logc) approximation factor. This improves the previous &THgr;(log |X|) bound of the greedy method and beats recent complexity-theoretic lower bounds for set covers (which don't make any assumptions about VC-dimension). We give several applications of our method to computational geometry, and we show that in some cases, such as those that arise in 3-d polytope approximation and 2-d disc covering, we can quickly find O(c)-sized covers.