J. D. Ullman and M. Yannakakis. The input/output complexity of transitive closure. Annals of Mathematics and Artificial Intelligence, 3:331--360, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....were designed for a theoretical RAM model with unlimited memory. It has been observed by many researchers that most of these algorithms perform very badly when used in an external memory setting. This led to the design of algorithms and data structures for external memory [CGG 95, Arg96b, UY91] Various theoretical results have been obtained in the last years starting with classical sorting and searching problems [AV88] Very recently a few researchers also considered practical implementations. One of the first external memory libraries was TPIE [VV95] TPIE consists of several so ....

....Buffer Heaps versus Radix Heaps b insert b delmin r insert r delmin Figure 4.14: Buffer Heaps versus Radix Heaps 37 5 Matrix Operations Matrix operations are a classical external memory application. We introduce a simple external memory algorithm for matrix multiplication. It is based on [UY91] So far, we do not provide special algorithms for sparse matrix multiplication. Our algorithm is quite simple. We divide each matrix M Theta M sub matrices. After this preprocessing step we simple multiply sub matrices with the standard matrix multiplication algorithm. This leads to a O(n ....

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Ullman and Yannakakis. The Input/Output Complexity of Transitive Closure. Annals of Mathematics and Artificial Intelligence, 3:331--360, 1991.

....to our problem, but in practice this cannot be done efficiently. For one, the algorithms are designed to perform transitive closure queries at runtime. An input query is a set of vertices Q V , and the output is the set of all vertices R V reachable from this set. Ullman and Yannakakis [UY91] obtain a bound of O(N 3 = p M ) I Os for computing the transitive closure of a graph with N nodes and main memoryM . The runtime performance hit could be solved by pre computing the transitive closure and storing it on disk. However, the space required by such a scheme would be huge (O(V ....

J. Ullman and M. Yannakakis. The input/output complexity of transitive closure. Annals of Mathematics and Artificial Intelligence 3, pages 331--360, 1991.

....has almost no effect on the accuracy of the BSP model. We modified the APSP algorithm described in [8] in order to obtain good overall performance. The original algorithm consisted of n iterations, each involving 2 # log p startups. The modified algorithm is derived from the algorithm given in [12]. Briefly, it consists of p p iterations in which 0 50 100 150 200 400 800 1200 1600 2000 Time per element (us) Matrix dimension n p = 16, measured p = 16, predicted p = 100, measured p = 100, predicted Figure 9. Predicted and measured communication times per element for APSP. the ....

J. Ullman and M. Yannakakis. The Input/Output Complexity of Transitive Closure. Annals of Mathematics and Artificial Intelligence, 3, 1991.

....paging algorithm that minimized the competitive ratio [4] Alternatively, all the work done in the database community on B trees could be viewed as a solution to our problem for complete trees with s = 1. Ullman and Yannakakis considered the I O complexity of the transitive closure problem [5] with block size B = 1. Their work differs from this in that they do not explicitly consider blocking, and that their lower bounds only need to consider the graph structure, and not an adversary trying to generate a path that will cause many page faults. There is considerable previous work on the ....

Jeffrey D. Ullman and Mihalis Yannakakis, The Input/Output Complexity of Transitive Closure, Annals of Mathematics and Artificial Intelligence (1991), 331--360.

....sort algorithm, we modified the APSP algorithm described in [JW96a] in order to obtain good overall performance. The original algorithm consisted of n iterations, and each iteration involved 2 Delta log p startups. The modified algorithm is derived from the external memory algorithm given in [UY91] Briefly, it consists of p p iterations, and in each iteration the transitive closure of the diagonal block is computed and broadcast to all processors in a binary tree fashion. Unbalanced communication occurs at the top levels of the broadcast tree, since at that point of the algorithm only a ....

J.D. Ullman and M. Yannakakis. The Input/Output Complexity of Transitive Closure. Annals of Mathematics and Artificial Intelligence, 3:331--360, 1991.

....almost no effect on the accuracy of the BSP model. We modified the APSP algorithm described in [8] in order to obtain good overall performance. The original algorithm consisted of n iterations, each involving 2 Delta log p startups. The modified algorithm is derived from the algorithm given in [12]. Briefly, it consists of p p iterations in which 0 50 100 150 200 400 800 1200 1600 2000 Matrix dimension n p = 16, measured p = 16, predicted p = 100, measured p = 100, predicted Figure 9. Predicted and measured communication times per element for APSP. the transitive closure of the ....

J. Ullman and M. Yannakakis. The Input/Output Complexity of Transitive Closure. Annals of Mathematics and Artificial Intelligence, 3, 1991.

....14, 15, 17, 38] Also, a general connection between the comparison complexity and the I O complexity of a given problem is shown in [4] More recently, external memory research has moved towards solving graph and geometric problems. Work on graph problems includes transitive closure computations [35], some graph traversal problems [23] and memory management problems for maintaining connectivity information and paths on graphs [19] Recently, Chiang et al. 12] present a collection of new techniques for designing and analyzing I O efficient graph algorithms, and apply these techniques to a ....

J. D. Ullman and M. Yannakakis. The input/output complexity of transitive closure. Annals of Mathematics and Artificial Intelligence, 3:331--360, 1991.

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J. D. Ullman and M. Yannakakis. The input/output complexity of transitive closure. Annals of Mathematics and Artificial Intelligence, 3:331--360, 1991.

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J. D. Ullman and M. Yannakakis. The input/output complexity of transitive closure. Annals of Mathematics and Artificial Intelligence, 3: 331-360, 1991.

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