Cache-Oblivious Streaming B-Trees

Abstract

A streaming B-tree is a dictionary that efficiently implements insertions and range queries. We present two cache-oblivious streaming B-trees, the shuttle tree, and the cache-oblivious lookahead array (COLA). For block-transfer size B and on N elements, the shuttle tree implements searches in optimal \(O(log_{B+1}N)\) transfers, range queries of L successive elements in optimal \(O(log_{B+1}N +L/B)\) transfers, and insertions in \(O((log_{B+1}N)/B^{\Theta(1/(log log B)^2)}+(log^2N)/B)\) transfers, which is an asymptotic speedup over traditional B-trees if \(B ≥ (log N)^{1+c log log log^2 N}\) for any constant c >1. A COLA implements searches in O(log N) transfers, range queries in O(log N + L/B) transfers, and insertions in amortized O((log N)/B) transfers, matching the bounds for a (cache-aware) buffered repository tree. A partially deamortized COLA matches these bounds but reduces the worst-case insertion cost to O(log N) if memory size \(M = \Omega(log N)\). We also present a cache-aware version of the COLA, the lookahead array, which achieves the same bounds as Brodal and Fagerberg's (cache-aware) \(B^{\epsilon}\)-tree. We compare our COLA implementation to a traditional B-tree. Our COLA implementation runs 790 times faster for random insertions, 3.1 times slower for insertions of sorted data, and 3.5 times slower for searches.