Abstract. This paper presents two dynamic search trees attaining near-optimal performance on any hierarchical memory. The data structures are independent of the parameters of the memory hierarchy, e.g., the number of memory levels, the block-transfer size at each level, and the relative speeds of memory levels. The performance is analyzed in terms of the number of memory transfers between two memory levels with an arbitrary block-transfer size of B; this analysis can then be applied to every adjacent pair of levels in a multilevel memory hierarchy. Both search trees match the optimal search bound of Θ(1+logB+1 N) memory transfers. This bound is also achieved by the classic B-tree data structure on a two-level memory hierarchy with a known block-transfer size B. The first search tree supports insertions and deletions in Θ(1 + logB+1 N) amortized memory transfers, which matches the B-tree’s worst-case bounds. The second search tree supports scanning S consecutive elements optimally in Θ(1 + S/B) memory transfers and supports insertions and deletions in Θ(1 + logB+1 N + log2 N) amortized memory transfers, matching the performance of the B-tree for B = B Ω(log N log log N).

The cache-oblivious model of computation is a two-level memory model with the assumption that the parameters of the model are unknown to the algorithms. A consequence of this assumption is that an algorithm efficient in the cache oblivious model is automatically efficient in a multi-level memory model. Since the introduction of the cache-oblivious model by Frigo et al. in 1999, a number of algorithms and data structures in the model has been proposed and analyzed. However, less attention has been given to whether the nice theoretical proporities of cache-oblivious algorithms carry over into practice. This paper is an algorithmic engineering study of cache-oblivious sorting. We investigate a number of implementation issues and parameters choices for the cache-oblivious sorting algorithm Lazy Funnelsort by empirical methods, and compare the final algorithm with Quicksort, the established standard for comparison based sorting, as well as with recent cache-aware proposals. The main result is a carefully implemented cache-oblivious sorting algorithm, which we compare to the best implementation of Quicksort we can find, and find that it competes very well for input residing in RAM, and outperforms Quicksort for input on disk. 1

Abstract. Frigo, Leiserson, Prokop and Ramachandran in 1999 introduced the ideal-cache model as a formal model of computation for developing algorithms in environments with multiple levels of caching, and coined the terminology of cache-oblivious algorithms. Cache-oblivious algorithms are described as standard RAM algorithms with only one memory level, i.e. without any knowledge about memory hierarchies, but are analyzed in the two-level I/O model of Aggarwal and Vitter for an arbitrary memory and block size and an optimal off-line cache replacement strategy. The result are algorithms that automatically apply to multi-level memory hierarchies. This paper gives an overview of the results achieved on cache-oblivious algorithms and data structures since the seminal paper by Frigo et al. 1