Cache-Oblivious Iterated Predecessor Queries via Range Coalescing
Author(s)Demaine, Erik D; Gopal, Vineet; Hasenplaugh, William Cleaburn
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In this paper we develop an optimal cache-oblivious data structure that solves the iterated predecessor problem. Given k static sorted lists L[subscript 1],L[subscript 2],…,L[subscript k] of average length n 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(log[subscript B+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(kn) space, and preprocessing requires only O(kn / B) memory transfers with high probability, given a tall cache of size M=Ω(B[superscript 2]).
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Workshop on Algorithms and Data Structures, WADS 2015
Springer Berlin / Heidelberg
Demaine, Erik D., Vineet Gopal, and William Hasenplaugh. “Cache-Oblivious Iterated Predecessor Queries via Range Coalescing.” Algorithms and Data Structures. Ed. Frank Dehne, Jörg-Rüdiger Sack, and Ulrike Stege. Vol. 9214. Cham: Springer International Publishing, 2015. 249–262.
Author's final manuscript