A general approach for cache-oblivious range reporting and approximate range counting

We present cache-oblivious solutions to two important variants of range searching: range reporting and approximate range counting. Our main contribution is a general approach for constructing cacheoblivious data structures that provide relative (1+ε)-approximations for a general class of range counting queries. This class includes three-sided range counting, 3-d dominance counting, and 3-d halfspace range counting. The constructed data structures use linear space and answer queries in the optimal query bound of O(logB(N/K)) block transfers in the worst case, where K is the number of points in the query range. As a corollary, we also obtain the first approximate 3-d halfspace range counting and 3-d dominance counting data structures with a worst-case query time of O(log (N/K)) in internal memory. An easy but important consequence of our main result is the existence of O(N log N)-space cacheoblivious data structures with an optimal query bound of O(logB N + K/B) block transfers for th...

• Type: Conference
• Year: 2009
• Where: COMPGEOM
• Authors: Peyman Afshani, Chris H. Hamilton, Norbert Zeh
• Keywords: COMPGEOM 2009, Data Structures, Discrete Geometry, Halfspace Range Counting, Range Counting