Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes. We extend the recent theoretical model of (KDD 2009) for graph compression, and show how it can be employed for compression-friendly reordering of social networks and web graphs and for assigning document identifiers in inverted indexes. We design and implement a novel theoretically sound reordering algorithm that is based on recursive graph bisection. Our experiments show a significant improvement of the compression rate of graph and indexes over existing heuristics. The new method is relatively simple and allows efficient parallel and distributed implementations, which is demonstrated on graphs with billions of vertices and hundreds of billions of edges.
@cite_23 suggest a reordering algorithm, called Layered Label Propagation , to compress social networks. The algorithm is built on a scalable graph clustering technique by label propagation @cite_27 . The idea is to assign a label for every vertex of a graph based on the labels of its neighbors. The process is executed in rounds until no more updates take place. Since the standard label propagation described in @cite_27 tends to produce a giant cluster, the authors of @cite_23 construct a hierarchy of clusters. The vertices of the same cluster are then placed together in the final order.
@cite_27 @cite_23
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We propose an algorithm for finding overlapping community structure in very large networks. The algorithm is based on the label propagation technique of Raghavan, Albert and Kumara, but is able to detect communities that overlap. Like the original algorithm, vertices have labels that propagate between neighbouring vertices so that members of a community reach a consensus on their community membership. Our main contribution is to extend the label and propagation step to include information about more than one community: each vertex can now belong to up to v communities, where v is the parameter of the algorithm. Our algorithm can also handle weighted and bipartite networks. Tests on an independently designed set of benchmarks, and on real networks, show the algorithm to be highly effective in recovering overlapping communities. It is also very fast and can process very large and dense networks in a short time. This paper proposes a probabilistic graphical model for the problem of propagating labels in video sequences, also termed the label propagation problem. Given a limited amount of hand labelled pixels, typically the start and end frames of a chunk of video, an EM based algorithm propagates labels through the rest of the frames of the video sequence. As a result, the user obtains pixelwise labelled video sequences along with the class probabilities at each pixel. Our novel algorithm provides an essential tool to reduce tedious hand labelling of video sequences, thus producing copious amounts of useable ground truth data. A novel application of this algorithm is in semi-supervised learning of discriminative classifiers for video segmentation and scene parsing. The label propagation scheme can be based on pixel-wise correspondences obtained from motion estimation, image patch based similarities as seen in epitomic models or even the more recent, semantically consistent hierarchical regions. We compare the abilities of each of these variants, both via quantitative and qualitative studies against ground truth data. We then report studies on a state of the art Random forest classifier based video segmentation scheme, trained using fully ground truth data and with data obtained from label propagation. The results of this study strongly support and encourage the use of the proposed label propagation algorithm. We continue the line of research on graph compression started with WebGraph, but we move our focus to the compression of social networks in a proper sense (e.g., LiveJournal): the approaches that have been used for a long time to compress web graphs rely on a specific ordering of the nodes (lexicographical URL ordering) whose extension to general social networks is not trivial. In this paper, we propose a solution that mixes clusterings and orders, and devise a new algorithm, called Layered Label Propagation, that builds on previous work on scalable clustering and can be used to reorder very large graphs (billions of nodes). Our implementation uses overdecomposition to perform aggressively on multi-core architecture, making it possible to reorder graphs of more than 600 millions nodes in a few hours. Experiments performed on a wide array of web graphs and social networks show that combining the order produced by the proposed algorithm with the WebGraph compression framework provides a major increase in compression with respect to all currently known techniques, both on web graphs and on social networks. These improvements make it possible to analyse in main memory significantly larger graphs. We continue the line of research on graph compression started with WebGraph, but we move our focus to the compression of social networks in a proper sense (e.g., LiveJournal): the approaches that have been used for a long time to compress web graphs rely on a specific ordering of the nodes (lexicographical URL ordering) whose extension to general social networks is not trivial. In this paper, we propose a solution that mixes clusterings and orders, and devise a new algorithm, called Layered Label Propagation, that builds on previous work on scalable clustering and can be used to reorder very large graphs (billions of nodes). Our implementation uses task decomposition to perform aggressively on multi-core architecture, making it possible to reorder graphs of more than 600 millions nodes in a few hours. Experiments performed on a wide array of web graphs and social networks show that combining the order produced by the proposed algorithm with the WebGraph compression framework provides a major increase in compression with respect to all currently known techniques, both on web graphs and on social networks. These improvements make it possible to analyse in main memory significantly larger graphs.