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268
Deeper Inside PageRank
 INTERNET MATHEMATICS
, 2004
"... This paper serves as a companion or extension to the “Inside PageRank” paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniq ..."
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Cited by 208 (4 self)
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This paper serves as a companion or extension to the “Inside PageRank” paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniqueness, and convergence properties, possible alterations to the basic model, suggested alternatives to the traditional solution methods, sensitivity and conditioning, and finally the updating problem. We introduce a few new results, provide an extensive reference list, and speculate about exciting areas of future research.
PowerGraph: Distributed GraphParallel Computation on Natural Graphs
"... Largescale graphstructured computation is central to tasks ranging from targeted advertising to natural language processing and has led to the development of several graphparallel abstractions including Pregel and GraphLab. However, the natural graphs commonly found in the realworld have highly ..."
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Cited by 128 (4 self)
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Largescale graphstructured computation is central to tasks ranging from targeted advertising to natural language processing and has led to the development of several graphparallel abstractions including Pregel and GraphLab. However, the natural graphs commonly found in the realworld have highly skewed powerlaw degree distributions, which challenge the assumptions made by these abstractions, limiting performance and scalability. In this paper, we characterize the challenges of computation on natural graphs in the context of existing graphparallel abstractions. We then introduce the PowerGraph abstraction which exploits the internal structure of graph programs to address these challenges. Leveraging the PowerGraph abstraction we introduce a new approach to distributed graph placement and representation that exploits the structure of powerlaw graphs. We provide a detailed analysis and experimental evaluation comparing PowerGraph to two popular graphparallel systems. Finally, we describe three different implementation strategies for PowerGraph and discuss their relative merits with empirical evaluations on largescale realworld problems demonstrating order of magnitude gains. 1
GraphChi: Largescale Graph Computation On just a PC
 In Proceedings of the 10th USENIX conference on Operating Systems Design and Implementation, OSDI’12
, 2012
"... Current systems for graph computation require a distributed computing cluster to handle very large realworld problems, such as analysis on social networks or the web graph. While distributed computational resources have become more accessible, developing distributed graph algorithms still remains c ..."
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Cited by 115 (6 self)
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Current systems for graph computation require a distributed computing cluster to handle very large realworld problems, such as analysis on social networks or the web graph. While distributed computational resources have become more accessible, developing distributed graph algorithms still remains challenging, especially to nonexperts. In this work, we present GraphChi, a diskbased system for computing efficiently on graphs with billions of edges. By using a wellknown method to break large graphs into small parts, and a novel parallel sliding windows method, GraphChi is able to execute several advanced data mining, graph mining, and machine learning algorithms on very large graphs, using just a single consumerlevel computer. We further extend GraphChi to support graphs that evolve over time, and demonstrate that, on a single computer, GraphChi can process over one hundred thousand graph updates per second, while simultaneously performing computation. We show, through experiments and theoretical analysis, that GraphChi performs well on both SSDs and rotational hard drives. By repeating experiments reported for existing distributed systems, we show that, with only fraction of the resources, GraphChi can solve the same problems in very reasonable time. Our work makes largescale graph computation available to anyone with a modern PC. 1
Know your neighbors: Web spam detection using the web topology
 In Proceedings of SIGIR
, 2007
"... Web spam can significantly deteriorate the quality of search engine results. Thus there is a large incentive for commercial search engines to detect spam pages efficiently and accurately. In this paper we present a spam detection system that uses the topology of the Web graph by exploiting the link ..."
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Cited by 108 (9 self)
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Web spam can significantly deteriorate the quality of search engine results. Thus there is a large incentive for commercial search engines to detect spam pages efficiently and accurately. In this paper we present a spam detection system that uses the topology of the Web graph by exploiting the link dependencies among the Web pages, and the content of the pages themselves. We find that linked hosts tend to belong to the same class: either both are spam or both are nonspam. We demonstrate three methods of incorporating the Web graph topology into the predictions obtained by our base classifier: (i) clustering the host graph, and assigning the label of all hosts in the cluster by majority vote, (ii) propagating the predicted labels to neighboring hosts, and (iii) using the predicted labels of neighboring hosts as new features and retraining the classifier. The result is an accurate system for detecting Web spam that can be applied in practice to largescale Web data.
A survey on pagerank computing
 Internet Mathematics
, 2005
"... Abstract. This survey reviews the research related to PageRank computing. Components of a PageRank vector serve as authority weights for web pages independent of their textual content, solely based on the hyperlink structure of the web. PageRank is typically used as a web search ranking component. T ..."
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Cited by 106 (0 self)
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Abstract. This survey reviews the research related to PageRank computing. Components of a PageRank vector serve as authority weights for web pages independent of their textual content, solely based on the hyperlink structure of the web. PageRank is typically used as a web search ranking component. This defines the importance of the model and the data structures that underly PageRank processing. Computing even a single PageRank is a difficult computational task. Computing many PageRanks is a much more complex challenge. Recently, significant effort has been invested in building sets of personalized PageRank vectors. PageRank is also used in many diverse applications other than ranking. We are interested in the theoretical foundations of the PageRank formulation, in the acceleration of PageRank computing, in the effects of particular aspects of web graph structure on the optimal organization of computations, and in PageRank stability. We also review alternative models that lead to authority indices similar to PageRank and the role of such indices in applications other than web search. We also discuss linkbased search personalization and outline some aspects of PageRank infrastructure from associated measures of convergence to link preprocessing. 1.
Towards scaling fully personalized PageRank
 In Proceedings of the 3rd Workshop on Algorithms and Models for the WebGraph (WAW
, 2004
"... Abstract Personalized PageRank expresses backlinkbased page quality around userselected pages in a similar way as PageRank expresses quality over the entire Web. Existing personalized PageRank algorithms can however serve online queries only for a restricted choice of page selection. In this pape ..."
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Cited by 104 (2 self)
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Abstract Personalized PageRank expresses backlinkbased page quality around userselected pages in a similar way as PageRank expresses quality over the entire Web. Existing personalized PageRank algorithms can however serve online queries only for a restricted choice of page selection. In this paper we achieve full personalization by a novel algorithm that computes a compact database of simulated random walks; this database can serve arbitrary personal choices of small subsets of web pages. We prove that for a fixed error probability, the size of our database is linear in the number of web pages. We justify our estimation approach by asymptotic worstcase lower bounds; we show that exact personalized PageRank values can only be obtained from a database of quadratic size. 1
Piccolo: Building Fast, Distributed Programs with Partitioned Tables
"... Piccolo is a new datacentric programming model for writing parallel inmemory applications in data centers. Unlike existing dataflow models, Piccolo allows computation running on different machines to share distributed, mutable state via a keyvalue table interface. Piccolo enables efficient appli ..."
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Cited by 86 (3 self)
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Piccolo is a new datacentric programming model for writing parallel inmemory applications in data centers. Unlike existing dataflow models, Piccolo allows computation running on different machines to share distributed, mutable state via a keyvalue table interface. Piccolo enables efficient application implementations. In particular, applications can specify locality policies to exploit the locality of shared state access and Piccolo’s runtime automatically resolves writewrite conflicts using userdefined accumulation functions. Using Piccolo, we have implemented applications for several problem domains, including the PageRank algorithm, kmeans clustering and a distributed crawler. Experiments using 100 Amazon EC2 instances and a 12 machine cluster show Piccolo to be faster than existing data flow models for many problems, while providing similar faulttolerance guarantees and a convenient programming interface. 1
Efficient Aggregation for Graph Summarization
"... Graphs are widely used to model real world objects and their relationships, and large graph datasets are common in many application domains. To understand the underlying characteristics of large graphs, graph summarization techniques are critical. However, existing graph summarization methods are mo ..."
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Cited by 83 (5 self)
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Graphs are widely used to model real world objects and their relationships, and large graph datasets are common in many application domains. To understand the underlying characteristics of large graphs, graph summarization techniques are critical. However, existing graph summarization methods are mostly statistical (studying statistics such as degree distributions, hopplots and clustering coefficients). These statistical methods are very useful, but the resolutions of the summaries are hard to control. In this paper, we introduce two databasestyle operations to summarize graphs. Like the OLAPstyle aggregation methods that allow users to drilldown or rollup to control the resolution of summarization, our methods provide an analogous functionality for large graph datasets. The first operation, called SNAP, produces a summary graph by grouping nodes based on userselected node attributes and relationships. The second operation, called kSNAP, further allows users to control the resolutions of summaries and provides the “drilldown ” and “rollup ” abilities to navigate through summaries with different resolutions. We propose an efficient algorithm to evaluate the SNAP operation. In addition, we prove that the kSNAP computation is NPcomplete. We propose two heuristic methods to approximate the kSNAP results. Through extensive experiments on a variety of real and synthetic datasets, we demonstrate the effectiveness and efficiency of the proposed methods.
On Compressing Social Networks
"... Motivated by structural properties of the Web graph that support efficient data structures for in memory adjacency queries, we study the extent to which a large network can be compressed. Boldi and Vigna (WWW 2004), showed that Web graphs can be compressed down to three bits of storage per edge; we ..."
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Cited by 83 (2 self)
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Motivated by structural properties of the Web graph that support efficient data structures for in memory adjacency queries, we study the extent to which a large network can be compressed. Boldi and Vigna (WWW 2004), showed that Web graphs can be compressed down to three bits of storage per edge; we study the compressibility of social networks where again adjacency queries are a fundamental primitive. To this end, we propose simple combinatorial formulations that encapsulate efficient compressibility of graphs. We show that some of the problems are NPhard yet admit effective heuristics, some of which can exploit properties of social networks such as link reciprocity. Our extensive experiments show that social networks and the Web graph exhibit vastly different compressibility characteristics.
Graph summarization with bounded error
 In SIGMOD 2008: Proceedings of the 2008 ACM SIGMOD International Conference on Management of data
, 2008
"... We propose a highly compact twopart representation of a given graph G consisting of a graph summary and a set of corrections. The graph summary is an aggregate graph in which each node corresponds to a set of nodes in G, and each edge represents the edges between all pair of nodes in the two sets. ..."
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Cited by 78 (8 self)
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We propose a highly compact twopart representation of a given graph G consisting of a graph summary and a set of corrections. The graph summary is an aggregate graph in which each node corresponds to a set of nodes in G, and each edge represents the edges between all pair of nodes in the two sets. On the other hand, the corrections portion specifies the list of edgecorrections that should be applied to the summary to recreate G. Our representations allow for both lossless and lossy graph compression with bounds on the introduced error. Further, in combination with the MDL principle, they yield highly intuitive coarselevel summaries of the input graph G. We develop algorithms to construct highly compressed graph representations with small sizes and guaranteed accuracy, and validate our approach through an extensive set of experiments with multiple reallife graph data sets. To the best of our knowledge, this is the first work to compute graph summaries using the MDL principle, and use the summaries (along with corrections) to compress graphs with bounded error.