Cache-oblivious B-trees

摘要

This paper presents two dynamic search trees attaining near-optimal performance on any hierarchical memory. The data structures are independent of the parameters of the memory hierarchy, e. g., the number of memory levels, the block-transfer size at each level, and the relative speeds of memory levels. The performance is analyzed in terms of the number of memory transfers between two memory levels with an arbitrary block-transfer size of B; this analysis can then be applied to every adjacent pair of levels in a multilevel memory hierarchy. Both search trees match the optimal search bound of Theta(1+log(B+1) N) memory transfers. This bound is also achieved by the classic B-tree data structure on a two-level memory hierarchy with a known block-transfer size B. The first search tree supports insertions and deletions in Theta(1 + log(B+1) N) amortized memory transfers, which matches the B-tree's worst- case bounds. The second search tree supports scanning S consecutive elements optimally in Theta(1 +S/B) memory transfers and supports insertions and deletions in Theta(1 + log(B+1) N + log(2) N/ B) amortized memory transfers, matching the performance of the B-tree for B = Omega(log N log log N).