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FOCS
2009
IEEE
15 years 8 months ago
Orthogonal Range Reporting in Three and Higher Dimensions
In orthogonal range reporting we are to preprocess N points in d-dimensional space so that the points inside a d-dimensional axis-aligned query box can be reported efficiently. T...
Peyman Afshani, Lars Arge, Kasper Dalgaard Larsen
COMPGEOM
2010
ACM
15 years 6 months ago
Orthogonal range reporting: query lower bounds, optimal structures in 3-d, and higher-dimensional improvements
Orthogonal range reporting is the problem of storing a set of n points in d-dimensional space, such that the k points in an axis-orthogonal query box can be reported efficiently. ...
Peyman Afshani, Lars Arge, Kasper Dalgaard Larsen
CCCG
2009
15 years 2 months ago
Data Structures for Range Aggregation by Categories
We solve instances of a general class of problems defined as follows: Preprocess a set S of possibly weighted colored geometric objects (e.g. points/orthogonal segments/rectangles...
Saladi Rahul, Prosenjit Gupta, K. S. Rajan
CCCG
2008
15 years 2 months ago
Searching for Frequent Colors in Rectangles
We study a new variant of colored orthogonal range searching problem: given a query rectangle Q all colors c, such that at least a fraction of all points in Q are of color c, mus...
Marek Karpinski, Yakov Nekrich
STOC
2012
ACM
272views Algorithms» more  STOC 2012»
13 years 3 months ago
The cell probe complexity of dynamic range counting
In this paper we develop a new technique for proving lower bounds on the update time and query time of dynamic data structures in the cell probe model. With this technique, we pro...
Kasper Green Larsen