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Graph Sample and Hold: A Framework for BigGraph Analytics
"... Sampling is a standard approach in biggraph analytics; the goal is to efficiently estimate the graph properties by consulting a sample of the whole population. A perfect sample is assumed to mirror every property of the whole population. Unfortunately, such a perfect sample is hard to collect in c ..."
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Sampling is a standard approach in biggraph analytics; the goal is to efficiently estimate the graph properties by consulting a sample of the whole population. A perfect sample is assumed to mirror every property of the whole population. Unfortunately, such a perfect sample is hard to collect in complex populations such as graphs (e.g. web graphs, social networks), where an underlying network connects the units of the population. Therefore, a good sample will be representative in the sense that graph properties of interest can be estimated with a known degree of accuracy. While previous work focused particularly on sampling schemes to estimate certain graph properties (e.g. triangle count), much less is known for the case when we need to estimate various graph properties with the same sampling scheme. In this paper, we propose a generic stream sampling framework for biggraph analytics,
Parallel Triangle Counting and Enumeration using Matrix Algebra
"... Abstractâ€”Triangle counting and enumeration are important kernels that are used to characterize graphs. They are also used to compute important statistics such as clustering coefficients. We provide a simple exact algorithm that is based on operations on sparse adjacency matrices. By parallelizing th ..."
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Abstractâ€”Triangle counting and enumeration are important kernels that are used to characterize graphs. They are also used to compute important statistics such as clustering coefficients. We provide a simple exact algorithm that is based on operations on sparse adjacency matrices. By parallelizing the individual sparse matrix operations, we achieve a parallel algorithm for triangle counting. The algorithm is generalizable to triangle enumeration by modifying the semiring that underlies the matrix algebra. We present a new primitive, masked matrix multiplication, that can be beneficial especially for the enumeration case. We provide results from an initial implementation for the counting case along with various optimizations for communication reduction and load balance. I.
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)