Cache-Oblivious Data Structures and Algorithms for Undirected Breadth-First Search and Shortest Paths

Brodal, Gerth Stølting; Fagerberg, Rolf; Meyer, Ulrich; Zeh, Norbert

doi:10.7146/brics.v11i2.21827

Cited by 14 publications

(30 citation statements)

References 10 publications

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“…Brodal et al [9] gave a cache oblivious algorithm for BFS achieving the same worst case I/O bounds as MM BFS D. Their preprocessing is similar to that in MM BFS D, except that it produces a hierarchical clustering using the cache oblivious algorithms for sorting, spanning tree, Euler tour and list ranking. The BFS phase uses a data-structure that maintains a hierarchy of pools and provides the set of neighbours of the nodes in a BFS level efficiently.…”

Section: Computation Modelsmentioning

confidence: 99%

Improved external memory BFS implementations

Ajwani

Meyer

Osipov

2007

2007 Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX)

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Breadth first search (BFS) traversal on massive graphs in external memory was considered non-viable until recently, because of the large number of I/Os it incurs. Ajwani et al. [3] showed that the randomized variant of the o(n) I/O algorithm of Mehlhorn and Meyer [24] (MM BFS) can compute the BFS level decomposition for large graphs (around a billion edges) in a few hours for small diameter graphs and a few days for large diameter graphs. We improve upon their implementation of this algorithm by reducing the overhead associated with each BFS level, thereby improving the results for large diameter graphs which are more difficult for BFS traversal in external memory. Also, we present the implementation of the deterministic variant of MM BFS and show that in most cases, it outperforms the randomized variant. The running time for BFS traversal is further improved with a heuristic that preserves the worst case guarantees of MM BFS. Together, they reduce the time for BFS on large diameter graphs from days shown in [3] to hours. In particular, on line graphs with random layout on disks, our implementation of the deterministic variant of MM BFS with the proposed heuristic is more than 75 times faster than the previous best result for the randomized variant of MM BFS in [3].

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Section: Computation Modelsmentioning

confidence: 99%

Improved external memory BFS implementations

Ajwani

Meyer

Osipov

2007

2007 Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX)

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“…Recently, several further results have been obtained, e.g. [24,58,25,26,27,19,2,14,17,20,29,34]. See also the survey in [13].…”

Section: Cache-oblivious Modelmentioning

confidence: 93%

An Optimal Cache‐Oblivious Priority Queue and Its Application to Graph Algorithms

Arge

Bender²,

Demaine³

et al. 2007

SIAM J. Comput.

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We develop an optimal cache-oblivious priority queue data structure, supporting insertion, deletion, and delete-min operations in O(1 B log M/B N B) amortized memory transfers, where M and B are the memory and block transfer sizes of any two consecutive levels of a multilevel memory hierarchy. In a cache-oblivious data structure, M and B are not used in the description of the structure. Our structure is as efficient as several previously developed external memory (cache-aware) priority queue data structures, which all rely crucially on knowledge about M and B. Priority queues are a critical component in many of the best known external memory graph algorithms, and using our cache-oblivious priority queue we develop several cache-oblivious graph algorithms.

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“…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].…”

Section: Graph Algorithmsmentioning

confidence: 99%

Cache-Oblivious Algorithms and Data Structures

Brodal

2004

Algorithm Theory - SWAT 2004

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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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Cache-Oblivious Data Structures and Algorithms for Undirected Breadth-First Search and Shortest Paths

Cited by 14 publications

References 10 publications

Improved external memory BFS implementations

Improved external memory BFS implementations

An Optimal Cache‐Oblivious Priority Queue and Its Application to Graph Algorithms

Cache-Oblivious Algorithms and Data Structures

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