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16
STXXL: Standard template library for XXL data sets
 In: Proc. of ESA 2005. Volume 3669 of LNCS
, 2005
"... for processing huge data sets that can fit only on hard disks. It supports parallel disks, overlapping between disk I/O and computation and it is the first I/Oefficient algorithm library that supports the pipelining technique that can save more than half of the I/Os. STXXL has been applied both in ..."
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Cited by 41 (5 self)
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for processing huge data sets that can fit only on hard disks. It supports parallel disks, overlapping between disk I/O and computation and it is the first I/Oefficient algorithm library that supports the pipelining technique that can save more than half of the I/Os. STXXL has been applied both in academic and industrial environments for a range of problems including text processing, graph algorithms, computational geometry, gaussian elimination, visualization, and analysis of microscopic images, differential cryptographic analysis, etc. The performance of STXXL and its applications is evaluated on synthetic and realworld inputs. We present the design of the library, how its performance features are supported, and demonstrate how the library integrates with STL. KEY WORDS: very large data sets; software library; C++ standard template library; algorithm engineering 1.
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
I/Oefficient strong connectivity and depthfirst search for directed planar graphs
 In Proceedings of the 44th IEEE Symposium on Foundations of Computer Science
, 2003
"... We present the first I/Oefficient algorithms for the following fundamental problems on directed planar graphs: finding the strongly connected components, finding a simplepath 2 3separator, and computing a depthfirst spanning (DFS) tree. Our algorithms for the first two problems perform O(sort(N ..."
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Cited by 6 (6 self)
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We present the first I/Oefficient algorithms for the following fundamental problems on directed planar graphs: finding the strongly connected components, finding a simplepath 2 3separator, and computing a depthfirst spanning (DFS) tree. Our algorithms for the first two problems perform O(sort(N)) I/Os, where N = V + E and sort(N) = Θ((N/B)log M/B (N/B)) is the number of I/Os required to sort N elements. The DFSalgorithm performs O(sort(N)log(N/M)) I/Os, where M is the number of elements that fit into main memory. 1.
An Optimal CacheOblivious Priority Queue and its Application to Graph Algorithms
 SIAM JOURNAL ON COMPUTING
, 2007
"... We develop an optimal cacheoblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in $O(\frac{1}{B}\log_{M/B}\frac{N}{B})$ amortized memory transfers, where $M$ and $B$ are the memory and block transfer sizes of any two consecutive levels of a multilevel ..."
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Cited by 5 (0 self)
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We develop an optimal cacheoblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in $O(\frac{1}{B}\log_{M/B}\frac{N}{B})$ 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 cacheoblivious 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 (cacheaware) 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 cacheoblivious priority queue we develop several cacheoblivious graph algorithms.
Pruning spanners and constructing wellseparated pair decompositions in the presence of memory hierarchies
, 2010
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I/OEfficient Algorithms on NearPlanar Graphs
, 2011
"... Obtaining I/Oefficient algorithms for basic graph problems on sparse directed graphs has been a longstanding open problem. The best known algorithms for most basic problems on such graphs still require Ω(V) I/Os in the worst case, where V is the number of vertices in the graph. Nevertheless optima ..."
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Obtaining I/Oefficient algorithms for basic graph problems on sparse directed graphs has been a longstanding open problem. The best known algorithms for most basic problems on such graphs still require Ω(V) I/Os in the worst case, where V is the number of vertices in the graph. Nevertheless optimal O(sort(V)) I/O algorithms are known for special classes of sparse graphs, like planar graphs and grid graphs. It is hard to accept that a problem becomes difficult as soon as the graph contains a few deviations from planarity. In this paper we extend the class of graphs on which basic graph problems can be solved I/Oefficiently. We discuss several ways to transform graphs that are almost planar into planar graphs (given a suitable drawing), and based on those transformations we obtain the first I/Oefficient algorithms for directed graphs that are almost planar. Let G be a directed graph that is given as a planar subgraph (V, E) and a set of additional edges EC. Our main result is a singlesourceshortestpaths algorithm that runs in O(EC + sort(V + EC)) I/Os. When EC is small our algorithm is a significant improvement over the best previously known algorithms, which required Ω(V) I/Os. Alternatively, when G is given with a drawing with T crossings, we can compute singlesource shortest paths in O(sort(V + T)) I/Os. We obtain similar bounds for computing (strongly) connected components, breadthfirst and depthfirst traversals and topological ordering. Submitted:
Testing acyclicity and topological sorting in externalmemory
, 2004
"... There has been a considerable amount of work recently to develop externalmemory algorithms for fundamental graph algorithms. This is due the increasing size of data sets for many modern ..."
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There has been a considerable amount of work recently to develop externalmemory algorithms for fundamental graph algorithms. This is due the increasing size of data sets for many modern
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"... We present algorithms that solve a number of fundamental problems on planar directed graphs (planar digraphs) in O(sort(N)) I/Os, where sort(N) is the number of I/Os needed to sort N elements. The problems we consider are breadthfirst search, the singlesource shortest path problem, computing a dir ..."
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We present algorithms that solve a number of fundamental problems on planar directed graphs (planar digraphs) in O(sort(N)) I/Os, where sort(N) is the number of I/Os needed to sort N elements. The problems we consider are breadthfirst search, the singlesource shortest path problem, computing a directed ear decomposition of a strongly connected planar digraph, computing an open directed ear decomposition of a strongly connected biconnected planar digraph, and topologically sorting a planar directed acyclic graph.
Abstract
"... We present I/Oefficient algorithms for computing optimal separator partitions of planar graphs. Our main result shows that, given a planar graph G with N vertices and an integer r> 0, a vertex separator of size O (N / √ r) that partitions G into O(N/r) subgraphs of size at most r and boundary s ..."
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We present I/Oefficient algorithms for computing optimal separator partitions of planar graphs. Our main result shows that, given a planar graph G with N vertices and an integer r> 0, a vertex separator of size O (N / √ r) that partitions G into O(N/r) subgraphs of size at most r and boundary size O ( √ r) can be computed in O(sort(N)) I/Os, provided that M ≥ 56r log 2 B. Together with the planar embedding algorithm presented in the companion paper [27], this result is the basis for I/Oefficient solutions to many other fundamental problems on planar graphs, including breadthfirst search and shortest paths [5, 8], depthfirst search [6, 9], strong connectivity [9], and topological sorting [8]. Our second result shows that, given I/Oefficient solutions to these problems, a general separator algorithm for graphs with costs and weights on their vertices [3] can be made I/Oefficient. Many classical separator theorems are special cases of this result. In particular, our I/Oefficient version allows the computation of a separator as produced by our first separator algorithm, but without placing any constraints on r. 1