Efficient tree layout in a multilevel memory hierarchy

We consider the problem of laying out a tree or trie in a hierarchical memory, where the tree/trie has a fixed parent/child structure. The goal is to minimize the expected number of block transfers performed during a search operation, subject to a given probability distribution on the leaves. This problem was previously considered by Gil and Itai, who show optimal but high-complexity algorithms when the block-transfer size is known. We propose a simple greedy algorithm that is within an additive constant strictly less than 1 of optimal. We also present a relaxed greedy algorithm that permits more flexibility in the layout while decreasing performance (increasing the expected number of block transfers) by only a constant factor. Finally, we extend this latter algorithm to the cache-oblivious setting in which the block-transfer size is unknown to the algorithm; in particular this extension solves the problem for a multilevel memory hierarchy. The query performance of the cache-oblivious layout is within a constant factor of the query performance of the optimal layout with known block size.