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Vertex and Hyperedge Connectivity in Dynamic Graph Streams
"... A growing body of work addresses the challenge of processing dynamic graph streams: a graph is defined by a sequence of edge insertions and deletions and the goal is to construct synopses and compute properties of the graph while using only limited memory. Linear sketches have proved to be a powerfu ..."
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A growing body of work addresses the challenge of processing dynamic graph streams: a graph is defined by a sequence of edge insertions and deletions and the goal is to construct synopses and compute properties of the graph while using only limited memory. Linear sketches have proved to be a powerful technique in this model and can also be used to minimize communication in distributed graph processing. We present the first linear sketches for estimating vertex connectivity and constructing hypergraph sparsifiers. Vertex connectivity exhibits markedly different combinatorial structure than edge connectivity and appears to be harder to estimate in the dynamic graph stream model. Our hypergraph result generalizes the work of Ahn et al. (PODS 2012) on graph sparsification and has the added benefit of significantly simplifying the previous results. One of the main ideas is related to the problem of reconstructing subgraphs that satisfy a specific sparsity property. We introduce a more general notion of graph degeneracy and extend the graph reconstruction result of Becker et al. (IPDPS 2011). 1
Multicore Triangle Computations Without Tuning
"... Abstract—Triangle counting and enumeration has emerged as a basic tool in largescale network analysis, fueling the development of algorithms that scale to massive graphs. Most of the existing algorithms, however, are designed for the distributedmemory setting or the externalmemory setting, and ca ..."
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Abstract—Triangle counting and enumeration has emerged as a basic tool in largescale network analysis, fueling the development of algorithms that scale to massive graphs. Most of the existing algorithms, however, are designed for the distributedmemory setting or the externalmemory setting, and cannot take full advantage of a multicore machine, whose capacity has grown to accommodate even the largest of realworld graphs. This paper describes the design and implementation of simple and fast multicore parallel algorithms for exact, as well as approximate, triangle counting and other triangle computations that scale to billions of nodes and edges. Our algorithms are provably cachefriendly, easy to implement in a language that supports dynamic parallelism, such as Cilk Plus or OpenMP, and do not require parameter tuning. On a 40core machine with twoway hyperthreading, our parallel exact global and local triangle counting algorithms obtain speedups of 17–50x on a set of realworld and synthetic graphs, and are faster than previous parallel exact triangle counting algorithms. We can compute the exact triangle count of the Yahoo Web graph (over 6 billion edges) in under 1.5 minutes. In addition, for approximate triangle counting, we are able to approximate the count for the Yahoo graph to within 99.6 % accuracy in under 10 seconds, and for a given accuracy we are much faster than existing parallel approximate triangle counting implementations. I.
Sharedmemory parallelism can be simple, . . .
, 2015
"... Parallelism is the key to achieving high performance in computing. However, writing efficient and scalable parallel programs is notoriously difficult, and often requires significant expertise. To address this challenge, it is crucial to provide programmers with highlevel tools to enable them to de ..."
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Parallelism is the key to achieving high performance in computing. However, writing efficient and scalable parallel programs is notoriously difficult, and often requires significant expertise. To address this challenge, it is crucial to provide programmers with highlevel tools to enable them to develop solutions efficiently, and at the same time emphasize the theoretical and practical aspects of algorithm design to allow the solutions developed to run efficiently under all possible settings. This thesis addresses this challenge using a threepronged approach consisting of the design of sharedmemory programming techniques, frameworks, and algorithms for important problems in computing. The thesis provides evidence that with appropriate programming techniques, frameworks, and algorithms, sharedmemory programs can be simple, fast, and scalable, both in theory and in practice. The results developed in this thesis serve to ease the transition into the multicore era. The first part of this thesis introduces tools and techniques for deterministic
Declaration
, 2014
"... I Ilias Giechaskiel of Magdalene College, being a candidate for the M.Phil in Advanced Computer Science, hereby declare that this report and the work described in it are my own work, unaided except as may be specified below, and that the report does not contain material that has already been used to ..."
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I Ilias Giechaskiel of Magdalene College, being a candidate for the M.Phil in Advanced Computer Science, hereby declare that this report and the work described in it are my own work, unaided except as may be specified below, and that the report does not contain material that has already been used to any substantial extent for a comparable purpose. Total word count: 14,311 (excluding Appendices A and B)