Paper by Erik D. Demaine

Erik D. Demaine, Vineet Gopal, and William Hasenplaugh, “Cache-Oblivious Iterated Predecessor Queries via Range Coalescing”, in Proceedings of the 14th International Symposium on Algorithms and Data Structures (WADS 2015), Victoria, British Columbia, Canada, August 5–7, 2015, pages 249–262.

In this paper we develop an optimal cache-oblivious data structure that solves the iterated predecessor problem. Given k static sorted length-n lists L1, L2, …, Lk and a query value q, the iterated predecessor problem is to find the largest element in each list which is less than q. Our solution to this problem, called “range coalescing”, requires O(logB+1 n + k/B) memory transfers for a query on a cache of block size B, which is information-theoretically optimal. The range-coalescing data structure consumes O(k n) space, and preprocessing requires only O(k n/B) memory transfers with high probability, given a tall cache of size M = Ω(B2).

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Last updated March 27, 2017 by Erik Demaine.