Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic 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
Algorithms for generalized halfspace range searching and other intersection searching problems
Computational Geometry: Theory and Applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Rectangular matrix multiplication revisited
Journal of Complexity
A technique for adding range restrictions to generalized searching problems
Information Processing Letters
Fast rectangular matrix multiplication and applications
Journal of Complexity
On the Average Number of Maxima in a Set of Vectors and Applications
Journal of the ACM (JACM)
Dynamic subgraph connectivity with geometric applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
New Upper Bounds for Generalized Intersection Searching Problems
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Fast sparse matrix multiplication
ACM Transactions on Algorithms (TALG)
Colored intersection searching via sparse rectangular matrix multiplication
Proceedings of the twenty-second annual symposium on Computational geometry
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A (slightly) faster algorithm for klee's measure problem
Proceedings of the twenty-fourth annual symposium on Computational geometry
A (slightly) faster algorithm for Klee's measure problem
Computational Geometry: Theory and Applications
Approximating the volume of unions and intersections of high-dimensional geometric objects
Computational Geometry: Theory and Applications
Klee's measure problem on fat boxes in time ∂(n(d+2)/3)
Proceedings of the twenty-sixth annual symposium on Computational geometry
The mono- and bichromatic empty rectangle and square problems in all dimensions
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
An improved algorithm for Klee's measure problem on fat boxes
Computational Geometry: Theory and Applications
On Klee's measure problem for grounded boxes
Proceedings of the twenty-eighth annual symposium on Computational geometry
Range counting coresets for uncertain data
Proceedings of the twenty-ninth annual symposium on Computational geometry
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Let P be a set of n points in Rd, so that each point is colored by one of C given colors. We present algorithms for preprocessing P into a data structure that efficiently supports queries of the form: Given an axis-parallel box Q, count the number of distinct colors of the points of P ∩ Q. We present a general and relatively simple solution that has polylogarithmic query time and worst-case storage about O(nd). It is based on several interesting structural properties of the problem that we derive. We also show that for random inputs, the data structure requires almost linear expected storage. We then present several techniques for achieving space-time tradeoff. In R2, the most efficient solution uses fast matrix multiplication in the preprocessing stage. In higher dimensions we obtain a tradeoff using simpler mechanisms. We give a reduction from matrix multiplication to the offline version of problem, which shows that in R2 our time-space tradeoffs are close to optimal in the sense that improving them substantially would improve the best exponent of matrix multiplication. Finally, we present a generalized matrix multiplication problem and show its intimate relation to counting colors in boxes in any dimension.