Cache-oblivious range reporting with optimal queries requires superlinear space

We consider a number of range reporting problems in two and three dimensions and prove lower bounds on the amount of space used by any cache-oblivious data structure for these problems that achieves the optimal query bound of O(logB N + K/B) block transfers, where K is the size of the query output. The problems we study are three-sided range reporting, 3-d dominance reporting, and 3-d halfspace range reporting. We prove that, in order to achieve the above query bound or even a bound of f(logB N, K/B), for any monotonically increasing function f(·, ·), the data structure has to use Ω(N(log log N)ε ) space. This lower bound holds even for the expected size of any Las-Vegas-type data structure that achieves an expected query bound of at most f(logB N, K/B) block transfers. The exponent ε depends on the function f and on the range of permissible block sizes. Our result has a number of interesting consequences. The first one is a new type of separation between the I/O model and the ...

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