Dynamic planar convex hull operations in near-logarithmic amortized time
Journal of the ACM (JACM)
Simplex Range Searching and k Nearest Neighbors of a Line Segment in 2D
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
External Memory Data Structures
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
External memory data structures
Handbook of massive data sets
Computational Geometry: Theory and Applications
On approximating the depth and related problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
On approximate range counting and depth
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Note: Computing closest and farthest points for a query segment
Theoretical Computer Science
Constructing minimum-interference networks
Computational Geometry: Theory and Applications
Optimal halfspace range reporting in three dimensions
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Computing hereditary convex structures
Proceedings of the twenty-fifth annual symposium on Computational geometry
Cache-oblivious range reporting with optimal queries requires superlinear space
Proceedings of the twenty-fifth annual symposium on Computational geometry
A general approach for cache-oblivious range reporting and approximate range counting
Proceedings of the twenty-fifth annual symposium on Computational geometry
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries
Journal of the ACM (JACM)
Algorithms for memory hierarchies: advanced lectures
Algorithms for memory hierarchies: advanced lectures
Top-k queries on temporal data
The VLDB Journal — The International Journal on Very Large Data Bases
Convex hull of imprecise points in o(n log n) time after preprocessing
Proceedings of the twenty-seventh annual symposium on Computational geometry
Three problems about dynamic convex hulls
Proceedings of the twenty-seventh annual symposium on Computational geometry
Constructing interference-minimal networks
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Improved space bounds for cache-oblivious range reporting
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Minimizing the error of linear separators on linearly inseparable data
Discrete Applied Mathematics
Range searching on uncertain data
ACM Transactions on Algorithms (TALG)
Convex hull of points lying on lines in o(nlogn) time after preprocessing
Computational Geometry: Theory and Applications
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Given n points in three dimensions, we show how to answer halfspace range reporting queries in O(log n+k) expected time for an output size k. Our data structure can be preprocessed in optimal O(n log n) expected time. We apply this result to obtain the first optimal randomized algorithm for the construction of the $(\le k)$-level in an arrangement of n planes in three dimensions. The algorithm runs in O(n log n+nk2) expected time. Our techniques are based on random sampling. Applications in two dimensions include an improved data structure for "k nearest neighbors" queries and an algorithm that constructs the order-k Voronoi diagram in O(n log n+nk log k) expected time.