Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
The input/output complexity of sorting and related problems
Communications of the ACM
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Handbook of discrete and computational geometry
Journal of Computer and System Sciences
Deterministic sorting in O(nlog log n) time and linear space
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computational Geometry in C
Improved fast interger sorting in linear space
Information and Computation
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
Integer Sorting in 0(n sqrt (log log n)) Expected Time and Linear Space
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Trans-Dichotomous Algorithms Without Multiplication - Some Upper and Lower Bounds
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Faster deterministic sorting and searching in linear space
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Planar Point Location in Sublogarithmic Time
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Tight bounds for dynamic convex hull queries (again)
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Proceedings of the twenty-fourth annual symposium on Computational geometry
Well-separated pair decomposition in linear time?
Information Processing Letters
Counting inversions, offline orthogonal range counting, and related problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximate shortest path queries using Voronoi duals
Transactions on computational science IX
Approximate shortest path queries using Voronoi duals
Transactions on computational science IX
A fast algorithm for three-dimensional layers of maxima problem
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
SIAM Journal on Computing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We reexamine fundamental problems from computational geometry in theallword RAM model, where input coordinates are integers that fit in a machine word. We develop a new algorithm for offline point location, a two-dimensional analog of sorting where one needs to order points with respect to segments. This result implies, for example, that the Voronoi diagram of n points in the plane can be constructed in (randomized) time n· 2O(√ lg lg n). Similar bounds hold for numerous other geometric problems, such as three-dimensional convex hulls, planar Euclidean minimum spanning trees, line segment intersection, and triangulation of non-simple polygons. In FOCS'06, we developed a data structure for online point location, which implied a bound of O(n (lg n)/(lg lg n) for Voronoi diagrams and the other problems. Our current bounds are dramatically better, and a convincing improvement over the classic O(n lg n) algorithms. As in the field of integer sorting, the main challenge is to find ways to manipulate information, while avoiding the online problem (in that case, predecessor search).