Abstract. We study the problem of maintaining a dynamic ordered set subject to insertions, deletions, and traversals of k consecutive elements. This problem is trivially solved on a RAM and on a simple two-level memory hierarchy. We explore this traversal problem on more realistic memory models: the cache-oblivious model, which applies to unknown and multi-level memory hierarchies, and sequential-access models, where sequential block transfers are less expensive than random block transfers. 1

An experimental comparison of cache aware and cache oblivious static search tree algorithms is presented. Both cache aware and cache oblivious algorithms outperform classic binary search on large data sets because of their better utilization of cache memory. Cache aware algorithms with implicit pointers perform best overall, but cache oblivious algorithms do almost as well and do not have to be tuned to the memory block size as cache aware algorithms require. Program instrumentation techniques are used to compare the cache misses and instruction counts for implementations of these algorithms.

Modern computer systems have increasingly complex memory systems. Common machine models for algorithm analysis do not reflect many of the features of these systems, e.g., large register sets, lockup-free caches, cache hierarchies, associativity, cache line fetching, and streaming behavior. Inadequate models lead to poor algorithmic choices and an incomplete understanding of algorithm behavior on real machines. A key step toward developing better models is to quantify the performance effects of features not reflected in the models. This paper explores the effect of memory system features on sorting performance. We introduce a new cache-conscious sorting algorithm, R-merge, which achieves better performance in practice over algorithms that are superior in the theoretical models. R-merge is designed to minimize memory stall cycles rather than cache misses by considering features common to many system designs.

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