## Cache-oblivious algorithms and data structures (2004)

Venue: | IN SWAT |

Citations: | 8 - 1 self |

### BibTeX

@INPROCEEDINGS{Brodal04cache-obliviousalgorithms,

author = {Gerth Stølting Brodal},

title = {Cache-oblivious algorithms and data structures},

booktitle = {IN SWAT},

year = {2004},

publisher = {}

}

### OpenURL

### 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.

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Citation Context ...ts optimized for the memory hierarchy—see e.g. the paper by Chatterjee et al. [35] and the references it contains.Ladner et al. considered the effect of caches in connection with heaps [54], sorting =-=[55]-=-, and sequential and random traversals [52]. Using registers to improve the running time of sorting was considered in [14]. Minimizing translation look-aside buffer (TLB) misses, and the case of low c... |

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Citation Context ... +√V E/B · √ V B/E ε ) I/Os respectively. Undirected single source shortest path (SSSP) can be solved cache-obliviously in O(V +E/B log(E/B)) I/Os [32,37], matching the known bounds for the I/O model =-=[51]-=-. V B E7 Computational geometry Goodrich et al. [45] introduced the distribution sweeping approach to solve a sequence of problems within computational geometry in the I/O model. A cacheoblivious ver... |

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Citation Context ...31,53,59]. Dynamic B-trees were first presented by Bender et al. [22] achieving searches in O(log B N) I/Os and updates requiring amortized O(log B N) I/Os. Simplified constructions were presented in =-=[23]-=- and [31], where [31] is based on combining the recursive static layout of Prokop [60] and the dynamic search trees of low height by Andersson and Lai [8], and [23] is based on combining the static la... |

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Citation Context ... of a given element. The layout of arbitrary static trees was considered in [20]. Finally, optimal cache-oblivious implicit dictionaries were developed in [42] and [43]. 5 Priority queues Arge et al. =-=[11]-=- presented the first cache-oblivious priority, supporting inserts and delete-min operations in O( 1 B logM/B N B ) I/Os. This matches the performance achieved in the I/O model by e.g. the buffer trees... |

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Citation Context ...m can achieve a performance better than log 2 e · log B N I/Os, i.e. a factor ≈ 1.44 slower than a cache-aware algorithm. Cache oblivious search trees avoiding the usage of pointers were presented in =-=[31,53,59]-=-. Dynamic B-trees were first presented by Bender et al. [22] achieving searches in O(log B N) I/Os and updates requiring amortized O(log B N) I/Os. Simplified constructions were presented in [23] and ... |

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Citation Context ...odel achieved in [36]. For directed BFS and DFS on general graphs a cache-oblivious algorithm was presented performing O((V + E/B)logV +Sort(E)) I/Os, matching the known best bounds for the I/O model =-=[34]-=-. For undirected DFS, an algorithm performing O(V + Sort(E)) I/Os was achieved, matching the bound for the I/O model in [58]. Finally an O(Sort(E)log log V ) I/O minimum spanning tree algorithm was pr... |

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Citation Context ... based on the merging paradigm, Funnelsort, and one based on the distribution paradigm. Both algorithms require the tall cache assumption M ≥ B 2 . A simplified version of Funnelsort was presented in =-=[28]-=-, denoted Lazy Funnelsort, requiring the tall cache assumption M ≥ B 1+ε . An empirical study of the developed cache-oblivious sorting algorithms is presented in [33]. That I/O optimal cache-oblivious... |

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Citation Context ...l by e.g. the buffer trees of Arge [10]. The construction in [11] is a general reduction to sorting. An alternative cache-oblivious priority achieving the same I/O complexity as [11] was presented in =-=[29]-=-. This solution is a more direct solution based on k-mergers introduced in the Funnelsort algorithm [44,28]. 6 Graph algorithms The existence of a cache-oblivious priority queue enabled a sequence of ... |

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Citation Context ....g. the paper by Chatterjee et al. [35] and the references it contains.Ladner et al. considered the effect of caches in connection with heaps [54], sorting [55], and sequential and random traversals =-=[52]-=-. Using registers to improve the running time of sorting was considered in [14]. Minimizing translation look-aside buffer (TLB) misses, and the case of low cache associativity was studied in [73]. Rah... |