Showing papers by "Rolf Fagerberg published in 2002"

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.For storing n elements, our proposal uses (1 + e)n times the element size of memory, and performs searches in worst case O(logBn) memory transfers, updates in amortized O((log2n)/(eB)) memory transfers, and range queries in worst case O(logBn + k/B) memory transfers, where k is the size of the output.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.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.

Cache Oblivious Distribution Sweeping

Abstract: We adapt the distribution sweepingmetho d to the cache oblivious model. Distribution sweepingis the name used for a general approach for divide-and-conquer algorithms where the combination of solved subproblems can be viewed as a merging process of streams. We demonstrate by a series of algorithms for specific problems the feasibility of the method in a cache oblivious setting. The problems all come from computational geometry, and are: orthogonal line segment intersection reporting, the all nearest neighbors problem, the 3D maxima problem, computingthe measure of a set of axis-parallel rectangles, computingthe visibility of a set of line segments from a point, batched orthogonal range queries, and reportingpairwise intersections of axis-parallel rectangles. Our basic buildingblo ck is a simplified version of the cache oblivious sorting algorithm Funnelsort of Frigo et al., which is of independent interest.

Funnel Heap - A Cache Oblivious Priority Queue

Abstract: 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 Arge et al recently presented the first optimal cache oblivious priority queue, and demonstrated the importance of this result by providingthe first cache oblivious algorithms for graph problems Their structure uses cache oblivious sorting and selection as subroutines In this paper, we devise an alternative optimal cache oblivious priority queue based only on binary merging We also show that our structure can be made adaptive to different usage profiles

Cache Oblivious Distribution Sweeping

Abstract: We adapt the distribution sweeping method to the cache oblivious model. Distribution sweeping is the name used for a general approach for divide-and-conquer algorithms where the combination of solved subproblems can be viewed as a merging process of streams. We demonstrate by a series of algorithms for specific problems the feasibility of the method in a cache oblivious setting. The problems all come from computational geometry, and are: orthogonal line segment intersection reporting, the all nearest neighbors problem, the 3D maxima problem, computing the measure of a set of axis-parallel rectangles, computing the visibility of a set of line segments from a point, batched orthogonal range queries, and reporting pairwise intersections of axis-parallel rectangles. Our basic building block is a simplified version of the cache oblivious sorting algorithm Funnelsort of Frigo et al., which is of independent interest. Full text: http://dx.doi.org/10.1007/3-540-45465-9_37

Computing Refined Buneman Trees in Cubic Time

Abstract: Reconstructing the evolutionary tree for a set of n species based on pairwise distances between the species is a fundamental problem in bioinformatics. Neighbour joining is a popular distance based tree reconstruction method. It always proposes fully resolved binary trees despite missing evidence in the underlying distance data. Distance based methods based on the theory of Buneman trees and refined Buneman trees avoid this problem by only proposing evolutionary trees whose edges satisfy a number of constraints. These trees might not be fully resolved but there is strong combinatorial evidence for each proposed edge. The currently best algorithm for computing the refined Buneman tree from a given distance measure has a running time of O(n^5) and a space consumption of O(n^4). In this paper, we present an algorithm with running time O(n^3) and space consumption O(n^2).