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## Mining Tera-Scale Graphs: Theory, engineering and discoveries (2012)

Citations: | 1 - 0 self |

### Citations

834 | The space complexity of approximating the frequency moments.
- Alon, Matias, et al.
- 1999
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Citation Context ...007, Charikar et al., 2000, Garofalakis and Gibbons, 2001]), we choose the Flajolet-Martin algorithm because it gives an unbiased estimate, as well as a tight O(log n) bound for the space complexity [=-=Alon et al., 1996-=-]. The main idea of Flajolet-Martin algorithm is as follows. We maintain a bitstring BITMAP[0 . . . L − 1] of length L which encodes the set. For each item to add, we do the following: 1. Pick an inde... |

445 |
The approximation of one matrix by another of lower rank.
- Eckart, Young
- 1936
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Citation Context ...es of A. The SVD is a very powerful tool in analyzing graphs as well as matrices [Kamel, 1984, Berry., 1992]; some of its applications include optimal matrix approximation in the least squares sense [=-=Eckart and Young, 1936-=-], Principal Component Analysis [Pearson, 1901], clustering [Zha et al., 2002] (more specifically a relaxed version of the well known k-means clustering problem) and Information Retrieval/Latent Seman... |

264 | The webgraph framework I: compression techniques - Boldi, Vigna - 2004 |

114 | Using Pagerank to characterize Web structure - Pandurangan, Raghavan, et al. - 2002 |

80 | Efficient MATLAB computations with sparse and factored tensors - Bader, Kolda - 2007 |

67 | Residual splash for optimally parallelizing belief propagation - Gonzalez, Low, et al. - 2009 |

58 | Latent Semantic Indexing is an Optimal Special Case of Multidimensional Scaling
- Brian, Bartell, et al.
- 1992
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Citation Context ... Berry., 1992], spectral clustering [Shi and Malik, 1997, Ng et al., 2002, Luxburg, 2007], Principal Component Analysis (PCA) [Pearson, 1901], Multi Dimensional Scaling (MDS) [Kruskal and Wish, 1978, =-=Bartell et al., 1992-=-], Latent Semantic Indexing (LSI) [Deerwester et al., 1990], and tensor analysis [Sun et al., 2006b, Kolda and Sun, 2008, Kolda and Bader, 2009, Dunlavy et al., 2011]. Despite their importance, existi... |

50 | Fast counting of triangles in large real networks without counting: Algorithms and laws
- Tsourakakis
- 2008
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Citation Context ...tral analysis is a fundamental tool not only for graph mining, but also for other areas of data mining. Eigenvalues and eigenvectors are at the heart of numerous algorithms such as triangle counting [=-=Tsourakakis, 2008-=-], Singular Value Decomposition (SVD) [Kamel, 1984, Berry., 1992], spectral clustering [Shi and Malik, 1997, Ng et al., 2002, Luxburg, 2007], Principal Component Analysis (PCA) [Pearson, 1901], Multi ... |

49 | On the streaming model augmented with a sorting primitive - Aggarwal, Datar, et al. - 2004 |

42 | Detecting fraudulent personalities in networks of online auctioneers - Chau, Pandit, et al. - 2006 |

30 | An Architecture for Recycling Intermediates in a Column-Store. In - Ivanova, Kersten, et al. - 2009 |

24 | Gbase: a scalable and general graph management system, in: - Kang, Tong, et al. - 2011 |

23 | Window-based tensor analysis on high-dimensional and multi-aspect streams. In:
- Sun, Papadimitriou, et al.
- 2006
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Citation Context ...omponent Analysis (PCA) [Pearson, 1901], Multi Dimensional Scaling (MDS) [Kruskal and Wish, 1978, Bartell et al., 1992], Latent Semantic Indexing (LSI) [Deerwester et al., 1990], and tensor analysis [=-=Sun et al., 2006-=-b, Kolda and Sun, 2008, Kolda and Bader, 2009, Dunlavy et al., 2011]. Despite their importance, existing eigensolvers do not scale well. As described in Section 6.7, the maximum order and size of inpu... |

12 | GConnect: A Connectivity Index for Massive Disk-Resident Graphs,” - Aggarwal, Yu - 2009 |

10 | Eigenspokes: Surprising patterns and community structure in large graphs - Prakash, Seshadri, et al. - 2010 |

6 |
A parallel algorithm to compute the shortest paths and diameter of a graph and its vlsi implementation
- Sinha, Bhattacharya, et al.
- 1986
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Citation Context ...hs, requiring O(|V | 2 + |V ||E|) and O(|V | 3 ) time. For the same reason, related BFS or all-pair shortest-path based algorithms like [Ferrez et al., 1998, Bader and Madduri, 2008, Ma and Ma, 1993, =-=Sinha et al., 1986-=-] can not handle large graphs. A sampling approach starts BFS from a subset of nodes, typically chosen at random as in [Broder et al., 2000]. Despite its practicality, this approach has no obvious sol... |

3 | Finding a maximum-weight induced k-partite subgraph of an i-triangulated graph
- Berry, Kennedy, et al.
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Citation Context ...tween the graph-level and individual node-level, there are also queries on the sub-graph level, e.g., community detection [Karypis and Kumar, 1999b, Andritsos et al., 2004], finding induced subgraph [=-=Addario-Berry et al., 2010-=-], etc. GBASE covers a wide range of queries, including the global and the node-level ones, by a unified matrix-vector multiplication framework. Column Store. Column-oriented DBMS has gained its popul... |

2 | 102 Hadoop information. http://hadoop.apache.org/. 104 Jama information. http://math.nist.gov/javanumerics/jama/. 102 Mahout information. http://lucene.apache.org/mahout/. 102 - edudocsdivisi2 |

2 | Plapack: Parallel linear algebra package - design overview. SC97 - Alvarez-Hamelin, Dall’Asta, et al. - 1997 |

2 | Graph structure in the web. Computer Networks 33 - Carlson, Betteridge, et al. - 2004 |

2 | URL citeseer.ist.psu.edu/ 164 - Garofalakis, Gibbons - 1985 |

1 | Percolation theory and fragmentation measures in social networks
- Chen, Paul, et al.
- 2007
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Citation Context ...(G) (at least 6.2× larger than their real world counterparts), meaning that they cannot be shattered quickly. 155et al., 2000] and characterizing real world graphs [Appel et al., 2009]. Chen et al. [=-=Chen et al., 2007-=-] studied the statistical behavior of a fragmentation measure from the removal of nodes in graphs. None of the previous works relate the shattering and the power law to the problem of node permutation... |

1 | A comparison of parallel algorithms for connected components - AISTAT - 1994 |