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14
Externalmemory breadthfirst search with sublinear I/O
 IN PROCEEDINGS OF THE 10TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS
, 2002
"... Breadthfirst search (BFS) is a basic graph exploration technique. We give the first external memory algorithm for sparse undirected graphs with sublinear I/O. The best previous algorithm requires \Theta (n + n+mD\Delta B \Delta logM=B n+mB) I/Os on a graph with n nodes and m edges and a machine w ..."
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Cited by 47 (13 self)
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Breadthfirst search (BFS) is a basic graph exploration technique. We give the first external memory algorithm for sparse undirected graphs with sublinear I/O. The best previous algorithm requires \Theta (n + n+mD\Delta B \Delta logM=B n+mB) I/Os on a graph with n nodes and m edges and a machine with mainmemory of size M, D parallel disks, and block size B. We present two versions of a new algorithm which requires only O i (p 1D\Delta B + p nm) \Delta n+mpD\Delta B \Delta logM=B n+mB
CacheOblivious Data Structures and Algorithms for Undirected BreadthFirst Search and Shortest Paths
 IN PROCEEDINGS OF THE 9TH SCANDINAVIAN WORKSHOP ON ALGORITHM THEORY
, 2004
"... We present improved cacheoblivious data structures and algorithms for breadthfirst search and the singlesource shortest path problem on undirected graphs with nonnegative edge weights. Our results close the performance gap between the currently best cacheaware algorithms for these problems and ..."
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Cited by 25 (9 self)
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We present improved cacheoblivious data structures and algorithms for breadthfirst search and the singlesource shortest path problem on undirected graphs with nonnegative edge weights. Our results close the performance gap between the currently best cacheaware algorithms for these problems and their cacheoblivious counterparts. Our shortestpath algorithm relies on a new data structure, called bucket heap, which is the first cacheoblivious priority queue to efficiently support a weak DecreaseKey operation.
A computational study of externalmemory BFS algorithms
 In SODA
, 2006
"... Breadth First Search (BFS) traversal is an archetype for many important graph problems. However, computing a BFS level decomposition for massive graphs was considered nonviable so far, because of the large number of I/Os it incurs. This paper presents the first experimental evaluation of recent exte ..."
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Cited by 18 (4 self)
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Breadth First Search (BFS) traversal is an archetype for many important graph problems. However, computing a BFS level decomposition for massive graphs was considered nonviable so far, because of the large number of I/Os it incurs. This paper presents the first experimental evaluation of recent externalmemory BFS algorithms for general graphs. With our STXXL based implementations exploiting pipelining and diskparallelism, we were able to compute the BFS level decomposition of a webcrawl based graph of around 130 million nodes and 1.4 billion edges in less than 4 hours using single disk and 2.3 hours using 4 disks. We demonstrate that some rather simple externalmemory algorithms perform significantly better (minutes as compared to hours) than internalmemory BFS, even if more than half of the input resides internally. 1
External Memory BFS on Undirected Graphs with Bounded Degree
 IN PROC. ACMSIAM SYMP. ON DISCRETE ALGORITHMS
, 2001
"... We give the first external memory algorithm for breadthfirst search (BFS) which achieves o(n) I/Os on arbitrary undirected graphs with n nodes and maximum node degree d. Let M and B > d denote the main memory size and block size, respectively. Using Sort(x) = ( x B log M=B x B ), our alg ..."
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Cited by 15 (5 self)
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We give the first external memory algorithm for breadthfirst search (BFS) which achieves o(n) I/Os on arbitrary undirected graphs with n nodes and maximum node degree d. Let M and B > d denote the main memory size and block size, respectively. Using Sort(x) = ( x B log M=B x B ), our algorithm needs O( n log d B + Sort(n B )) I/Os and O(n B ) external space for an arbitrary parameter 0 < 1=2. The result carries over to BFS, depthfirst search (DFS) and single source shortest paths (SSSP) on undirected planar graphs with arbitrary node degrees.
I/Oefficient undirected shortest paths
 In Proc. 11th Annual European Symposium on Algorithms, volume 2832 of LNCS
, 2003
"... Abstract. We show how to compute singlesource shortest paths in undirected graphs with nonnegative edge lengths in O ( p nm/B log n + MST (n, m)) I/Os, where n is the number of vertices, m is the number of edges, B is the disk block size, and MST (n, m) is the I/Ocost of computing a minimum spann ..."
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Cited by 11 (4 self)
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Abstract. We show how to compute singlesource shortest paths in undirected graphs with nonnegative edge lengths in O ( p nm/B log n + MST (n, m)) I/Os, where n is the number of vertices, m is the number of edges, B is the disk block size, and MST (n, m) is the I/Ocost of computing a minimum spanning tree. For sparse graphs, the new algorithm performs O((n / √ B) log n) I/Os. This result removes our previous algorithm’s dependence on the edge lengths in the graph. 1
Cacheoblivious algorithms and data structures
 IN SWAT
, 2004
"... Frigo, Leiserson, Prokop and Ramachandran in 1999 introduced the idealcache model as a formal model of computation for developing algorithms in environments with multiple levels of caching, and coined the terminology of cacheoblivious algorithms. Cacheoblivious algorithms are described as stand ..."
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Cited by 8 (1 self)
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Frigo, Leiserson, Prokop and Ramachandran in 1999 introduced the idealcache model as a formal model of computation for developing algorithms in environments with multiple levels of caching, and coined the terminology of cacheoblivious algorithms. Cacheoblivious 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 twolevel I/O model of Aggarwal and Vitter for an arbitrary memory and block size and an optimal offline cache replacement strategy. The result are algorithms that automatically apply to multilevel memory hierarchies. This paper gives an overview of the results achieved on cacheoblivious algorithms and data structures since the seminal paper by Frigo et al.
ExternalMemory Exact and Approximate AllPairs ShortestPaths in Undirected Graphs
, 2004
"... We present several new externalmemory algorithms for finding allpairs shortest paths in a Vnode, Eedge undirected graph. For allpairs shortest paths and diameter in unweighted undirected graphs we present cacheoblivious algorithnls with O(V. ~ log. ~ ~) I/Os, where B is the blocksize and M is ..."
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Cited by 4 (1 self)
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We present several new externalmemory algorithms for finding allpairs shortest paths in a Vnode, Eedge undirected graph. For allpairs shortest paths and diameter in unweighted undirected graphs we present cacheoblivious algorithnls with O(V. ~ log. ~ ~) I/Os, where B is the blocksize and M is the size of internal memory. For weighted tmdirected graphs we present a cacheaware APSP algorithm that performs O(V. ( V/ ~ + ~ log ~)) I/Os. We also present efficient cacheaware algorithms that find paths between all pairs of vertices in an unweighted graph with lengths within a small additive constant of the shortest path length. All of our results improve earlier results known for these problems. For approximate APSP we provide the first nontrivial results. Our diameter result uses C9(V + E) extra space, and all of our other algorithms use O(V 2) space. 1
Building a parallel pipelined external memory algorithm library
 In 23rd IEEE International Parallel & Distributed Processing Symposium (IPDPS
, 2009
"... Large and fast hard disks for little money have enabled the processing of huge amounts of data on a single machine. For this purpose, the wellestablished STXXL library provides a framework for external memory algorithms with an easytouse interface. However, the clock speed of processors cannot ke ..."
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Cited by 3 (1 self)
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Large and fast hard disks for little money have enabled the processing of huge amounts of data on a single machine. For this purpose, the wellestablished STXXL library provides a framework for external memory algorithms with an easytouse interface. However, the clock speed of processors cannot keep up with the increasing bandwidth of parallel disks, making many algorithms actually computebound. To overcome this steadily worsening limitation, we exploit today’s multicore processors with two new approaches. First, we parallelize the internal computation of the encapsulated external memory algorithms by utilizing the MCSTL library. Second, we augment the unique pipelining feature of the STXXL, to enable automatic task parallelization. We show using synthetic and practical use cases that the combination of both techniques increases performance greatly. 1
Cacheoblivious planar shortest paths
 In Proc. 32nd International Colloquium on Automata, Languages, and Programming. LNCS
, 2005
"... Abstract. We present an efficient cacheoblivious implementation of the shortestpath algorithm for planar graphs by Klein et al., and prove that it incurs no more than O ` N B1/2−ɛ + N B log N ´ block transfers on a graph with N vertices. This is the first cacheoblivious algorithm for this problem ..."
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Cited by 2 (1 self)
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Abstract. We present an efficient cacheoblivious implementation of the shortestpath algorithm for planar graphs by Klein et al., and prove that it incurs no more than O ` N B1/2−ɛ + N B log N ´ block transfers on a graph with N vertices. This is the first cacheoblivious algorithm for this problem that incurs o(N) block transfers. 1