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SODA
2008
ACM

Space-efficient dynamic orthogonal point location, segment intersection, and range reporting

8 years 3 months ago
Space-efficient dynamic orthogonal point location, segment intersection, and range reporting
We describe an asymptotically optimal data-structure for dynamic point location for horizontal segments. For n line-segments, queries take O(log n) time, updates take O(log n) amortized time and the data structure uses O(n) space. This is the first structure for the problem that is optimal in space and time (modulo the possibility of removing amortization). We also describe dynamic data structures for orthogonal range reporting and orthogonal intersection reporting. In both data structures for n points (segments) updates take O(log n) amortized time, queries take O(log n+k log n/ log log n) time, and the structures use O(n) space, where k is the size of the output. The model of computation is the unit cost RAM.
Guy E. Blelloch
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2008
Where SODA
Authors Guy E. Blelloch
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