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Cache-oblivious range reporting with optimal queries requires superlinear space. (English summary) Discrete Comput. Geom. 45 (2011), no. 4, 824–850. Summary: “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(log B 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(log B 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 also for the expected size of any Las-Vegas-type data structure that achieves an expected query bound of at most f(log B 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 separatio

Year: 2013

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