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17
External Memory Data Structures
, 2001
"... In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynami ..."
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Cited by 76 (32 self)
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In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.
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 57 (14 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
On External Memory MST, SSSP and Multiway Planar Graph Separation (Extended Abstract)
, 2000
"... Recently external memory graph algorithms have received considerable attention because massive graphs arise naturally in many applications involving massive data sets. Even though a large number of I/Oefficient graph algorithms have been developed, a number of fundamental problems still remain ..."
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Cited by 32 (11 self)
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Recently external memory graph algorithms have received considerable attention because massive graphs arise naturally in many applications involving massive data sets. Even though a large number of I/Oefficient graph algorithms have been developed, a number of fundamental problems still remain open. In this paper we develop improved algorithms for the problem of computing a minimum spanning tree of a general graph G = (V; E), as well as new algorithms for the single source shortest paths and the multiway graph separation problems on planar graphs.
On externalmemory MST, SSSP and multiway planar graph separation
 In Proc. 8th Scandinavian Workshop on Algorithmic Theory, volume 1851 of LNCS
, 2000
"... Recently external memory graph algorithms have received considerable attention because massive graphs arise naturally in many applications involving massive data sets. Even though a large number of I/Oefficient graph algorithms have been developed, a number of fundamental problems still remain open ..."
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Cited by 32 (2 self)
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Recently external memory graph algorithms have received considerable attention because massive graphs arise naturally in many applications involving massive data sets. Even though a large number of I/Oefficient graph algorithms have been developed, a number of fundamental problems still remain open. In this paper we develop an improved algorithm for the problem of computing a minimum spanning tree of a general graph, as well as new algorithms for the single source shortest paths and the multiway graph separation problems on planar graphs.
I/OEfficient Algorithms for Problems on Gridbased Terrains (Extended Abstract)
 In Proc. Workshop on Algorithm Engineering and Experimentation
, 2000
"... Lars Arge Laura Toma Jeffrey Scott Vitter Center for Geometric Computing Department of Computer Science Duke University Durham, NC 277080129 Abstract The potential and use of Geographic Information Systems (GIS) is rapidly increasing due to the increasing availability of massive amoun ..."
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Cited by 29 (13 self)
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Lars Arge Laura Toma Jeffrey Scott Vitter Center for Geometric Computing Department of Computer Science Duke University Durham, NC 277080129 Abstract The potential and use of Geographic Information Systems (GIS) is rapidly increasing due to the increasing availability of massive amounts of geospatial data from projects like NASA's Mission to Planet Earth. However, the use of these massive datasets also exposes scalability problems with existing GIS algorithms. These scalability problems are mainly due to the fact that most GIS algorithms have been designed to minimize internal computation time, while I/O communication often is the bottleneck when processing massive amounts of data.
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 26 (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
On ExternalMemory Planar Depth First Search
 Journal of Graph Algorithms and Applications
"... Even though a large number of I/Oefficient graph algorithms have been developed, a number of fundamental problems still remain open. For example, no space and I/Oefficient algorithms are known for depthfirst search or breadthfirst search in sparse graphs. In this paper we present two new re ..."
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Cited by 24 (14 self)
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Even though a large number of I/Oefficient graph algorithms have been developed, a number of fundamental problems still remain open. For example, no space and I/Oefficient algorithms are known for depthfirst search or breadthfirst search in sparse graphs. In this paper we present two new results on I/Oefficient depthfirst search in an important class of sparse graphs, namely undirected embedded planar graphs. We develop a new efficient depthfirst search algorithm and show how planar depthfirst search in general can be reduced to planar breadthfirst search. As part of the first result we develop the first I/Oefficient algorithm for finding a simple cycle separator of a biconnected planar graph. Together with other recent reducibility results, the second result provides further evidence that external memory breadthfirst search is among the hardest problems on planar graphs. 1
I/Oefficient algorithms for graphs of bounded treewidth
 In Proceedings of the 12th Annual ACMSIAM Symposium on Discrete Algorithms (SODA’2001
, 2001
"... We present an algorithm that takes O(sort(N)) I/Os 1 to compute a tree decomposition of width at most k, for any graph G of treewidth at most k and size N. Given such a tree decomposition, we use a dynamic programming framework to solve a wide variety of problems on G in O(N/(DB)) I/Os, including th ..."
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Cited by 16 (5 self)
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We present an algorithm that takes O(sort(N)) I/Os 1 to compute a tree decomposition of width at most k, for any graph G of treewidth at most k and size N. Given such a tree decomposition, we use a dynamic programming framework to solve a wide variety of problems on G in O(N/(DB)) I/Os, including the singlesource shortest path problem and a number of problems that are NPhard on general graphs. The tree decomposition can also be used to obtain an optimal separator decomposition of G. We use such a decomposition to perform depthfirst search in G in O(N/(DB)) I/Os. As important tools that are used in the tree decomposition algorithm, we introduce flippable DAGs and present an algorithm that computes a perfect elimination ordering of a ktree in O(sort(N)) I/Os. The second contribution of our paper, which is of independent interest, is a general and simple framework for obtaining I/Oefficient algorithms for a number of graph problems that can be solved using greedy algorithms in internal memory. We apply this framework in order to obtain an improved algorithm for finding a maximal matching and the first deterministic I/Oefficient algorithm for finding a maximal independent set of an arbitrary graph. Both algorithms take O(sort(V +E)) I/Os. The maximal matching algorithm is used in the tree decomposition algorithm.