Cache Oblivious Search Trees via Binary Trees of Small Height

Abstract

We propose a version of cache oblivious search trees which is simpler than the previous proposal of Bender, Demaine and Farach-Colton and has the same complexity bounds. In particular, our data structure avoids the use of weight balanced B-trees, and can be implemented as just a single array of data elements, without the use of pointers. The structure also improves space utilization.<br /> <br />For storing n elements, our proposal uses (1+epsilon)n times the element size of memory, and performs searches in worst case O(log_B n) memory transfers, updates in amortized O((log^2 n)/(epsilon B)) memory transfers, and range queries in worst case O(log_B n + k/B) memory transfers, where k is the size of the output.<br /> <br />The basic idea of our data structure is to maintain a dynamic binary tree of height log n + O(1) using existing methods, embed this tree in a static binary tree, which in turn is embedded in an array in a cache oblivious fashion, using the van Emde Boas layout of Prokop.<br /> <br />We also investigate the practicality of cache obliviousness in the area of search trees, by providing an empirical comparison of different methods for laying out a search tree in memory.<br /> <br />The source code of the programs, our scripts and tools, and the data we present here are available online under ftp.brics.dk/RS/01/36/Experiments/.