External-Memory Search Trees with Fast Insertions

This thesis provides both experimental and theoretical contributions regarding externalmemory 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 ǫ ∈ [1/ lgB, 1] this data structure achieves O((1/ǫB)(1+ logB(N/B))) block transfers for Insert and Delete and O((1/ǫ)(1 + logB(N/B))) block transfers for Search. The update complexity is amortized and is O((1/ǫ)(1+ logB(N/B))) in the worst case. Using the value ǫ = 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. This thesis also shows how to build a cache-oblivious data structure, the cacheoblivious lookahead array, which achieves the same bounds as the buffered repository B-tree in the case where ǫ = 1/ lgB. 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. Thesis Supervisor: Charles E. Leiserson Title: Professor of Computer Science and Engineering Thesis Supervisor: Bradley C. Kuszmaul Title: Research Scientist