External-memory search trees with fast insertions

Abstract

This thesis provides both experimental and theoretical contributions regarding external-memory dynamic search trees with fast insertions. The first contribution is the implementation of the buffered repository B-tree, a data structure that provably outperforms B-trees for updates at the cost of a constant factor decrease in query performance. This thesis also describes the cache-oblivious lookahead array, which outperforms B-trees for updates at a logarithmic cost in query performance, and does so without knowing the cache parameters of the system it is being run on. The buffered repository B-tree is an external-memory search tree that can be tuned for a tradeoff between queries and updates. Specifically, for any E [1/ lg B, 1] this data structure achieves O((1/EBl-E)(1 + logB(N/B))) block transfers for INSERT and DELETE and 0((/(1 + logB(N/B))) block transfers for SEARCH. The update complexity is amortized and is O((1/e)(1 + logB(N/B))) in the worst case. Using the value = 1/2, I was able to achieve a 17 times increase in insertion performance at the cost of only a 3 times decrease in search performance on a database with 12-byte items on a disk with a 4-kilobyte block size.

(cont.) This thesis also shows how to build a cache-oblivious data structure, the cache-oblivious lookahead array, which achieves the same bounds as the buffered repository B'-tree in the case where e = 1/ lg B. Specifically, it achieves an update complexity of O((1/B) log(N/B)) and a query complexity of O(log(N/B)) block transfers. This is the first data structure to achieve these bounds cache-obliviously. The research involving the cache-oblivious lookahead array represents joint work with Michael A. Bender, Jeremy Fineman, and Bradley C. Kuszmaul.