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

For many geometric problems, there are ecient algorithms that surprisingly use very little extra space other than the given array holding the input. For many geometric query problems, there are ecient data structures that need no extra space at all other than an array holding a permutation of the input. In this paper, we obtain the rst such space-economical solutions for a number of fundamental problems, including three-dimensional convex hulls, two-dimensional Delaunay triangulations, xed-dimensional range queries, and xed-dimensional nearest neighbor queries.

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

We examine the space requirement for the classic linesegment intersection problem. Using so-called implicit data structures, we show how to make the standard sweep-line algorithm run in O((n + k) log 2 n) time with only O(log 2 n) extra space, where n is the number of line segments and k is the number of intersections. If division is allowed and input can be destroyed, the algorithm can run in O((n + k) log n) time with O(1) extra space.

Abstract. Consider a data structure D that stores a dynamic collection of elements. Assume that D uses a linear number of words in addition to the elements stored. In this paper several data-structural transformations are described that can be used to transform D into another data structure D ′ that supports the same operations as D, has considerably smaller memory overhead than D, and performs the supported operations by a small constant factor or a small additive term slower than D, depending on the data structure and operation in question. The compaction technique has been successfully applied for linked lists, dictionaries, and priority queues.

Abstract We revisit a classic problem in computational geometry: preprocessing a planar n-point set to answer nearest neighbor queries. In SoCG 2004, Br"onnimann, Chan, and Chen showed that it is possible to design an efficient data structure that takes no extra space at all other than the input array holding a permutation of the points. The best query time known for such "in-place data structures " is O(log 2 n). In this paper, we break the O(log 2 n) barrier by providing a method that answers nearest neighbor queries in time O((log n) log3=2 2 log log n) = O(log

Abstract. The time required for a sequence of operations on a data structure is usually measured in terms of the worst possible such sequence. This, however, is often an overestimate of the actual time required. Distribution-sensitive data structures attempt to take advantage of underlying patterns in a sequence of operations in order to reduce time complexity, since access patterns are non-random in many applications. Unfortunately, many of the distribution-sensitive structures in the literature require a great deal of space overhead in the form of pointers. We present a dictionary data structure that makes use of both randomization and existing space-efficient data structures to yield very low space overhead while maintaining distribution sensitivity in the expected sense. 1

Data structure is a vital concept in computer science. In the last decades it has been inves-tigated from different points of views. However, one big problem with all these data structures that is too often overlooked is how horribly inefficient their space usage is. Nowadays, due to the exponential proliferation of information, especially the electronic data in the Internet environment and genome sequences in biology, there is an upsurging interest in the space-conscious algorithms, which requires us to consider space efficiency in designing data structures more seriously than ever before. Huge amount of theoretical work has been done in data structure compressions; however, the implementations of any known compressed data structures are not fully investigated. We believe that compressed data structures may become a crucial tool for the design of sophisticated and efficient software solutions. Therefore it is important to develop the basic tools supporting compressed data structures. In this thesis, we focused on the efficient implementation of succinct data structures, especially the RANK and SELECT functions. We did thorough experiments concerning the memory overhead, memory hierarchy and execution time of these implementations. Our experimental results showed

Abstract. In this paper we present an implicit dictionary with the working set property i.e. a dictionary supporting insert(e), delete(x) and predecessor(x) in O(log n) time and search(x) in O(log ℓ) time, where n is the number of elements stored in the dictionary and ℓ is the number of distinct elements searched for since the element with key x was last searched for. The dictionary stores the elements in an array of size n using no additional space. In the cache-oblivious model the operations insert(e), delete(x) and predecessor(x) cause O(log B n) cache-misses and search(x) causes O(log B ℓ) cache-misses. 1