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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).

In this paper, we present lower bounds for permuting and sorting in the cache-oblivious model. We prove that (1) I/O optimal cache-oblivious comparison based sorting is not possible without a tall cache assumption, and (2) there does not exist an I/O optimalcache-oblivious algorithm for permuting

The memory system of most modern computers consists of a hierarchy of memory levels, with each level acting as a cache for the next; for a typical desktop computer the hierarchy consists of registers, level 1 cache, level 2 cache, level 3 cache, main memory, and disk. One of the essential

structures with the optimal query bound and using linear or O(N log ∗ N) space are known for the above problems. The second consequence is the non-existence of a linear-space cache-oblivious persistent B-tree with worst-case optimal 1-d range reporting queries. Part of this work was done while visiting

A recent direction in the design of cache-efficient and diskefficient algorithms and data structures is the notion of cache obliviousness, introduced by Frigo, Leiserson, Prokop, and Ramachandran in 1999. Cache-oblivious algorithms perform well on a multilevel memory hierarchy without knowing any

1 Introduction Modern computers are characterized by having a memory system consisting ofa hierarchy of several levels of memory, where each level is acting as a cache for the next level [46]. The typical memory levels of current machines are registers,level 1 cache, level 2 cache, level 3 cache

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

Abstract. We present cache-oblivious data structures based upon exponential structures. These data structures perform well on a hierarchical memory but do not depend on any parameters of the hierarchy, including the block sizes and number of blocks at each level. The problems we consider

In this overview paper we motivate the need for and research issues arising from a new model of data processing. In this model, data does not take the form of persistent relations, but rather arrives in multiple, continuous, rapid, time-varying data streams. In addition to reviewing past work