Cache-oblivious dynamic dictionaries with update/query tradeoffs

Abstract

Several existing cache-oblivious dynamic dictionaries achieve O(logB N) (or slightly better O(logB N over M )) memory transfers per operation, where N is the number of items stored, M is the memory size, and B is the block size, which matches the classic B-tree data structure. One recent structure achieves the same query bound and a sometimes-better amortized update bound of O (...) memory transfers. This paper presents a new data structure, the xDict, implementing predecessor queries in O(...)worstcase memory transfers and insertions and deletions in O (...) amortized memory transfers, for any constant " with 0 < epsilon < 1. For example, the xDict achieves subconstant amortized update cost when N = ..., whereas the B-tree’s ... is subconstant only when ... is subconstant only when N = .... The xDict attains the optimal tradeoff between insertions and queries, even in the broader external-memory model, for the range where inserts cost between (...) and O(1= lg3 N) memory transfers.