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.

• Type: Conference
• Year: 2008
• Where: SODA
• Authors: Guy E. Blelloch
• Keywords: Algorithms, Amortized Time, Data Structures, Dynamic Point Location, SODA 2008