Tight and simple Web graph compression

Analysing Web graphs has applications in determining page ranks, fighting Web spam, detecting communities and mirror sites, and more. This study is however hampered by the necessity of storing a major part of huge graphs in the external memory, which prevents efficient random access to edge (hyperlink) lists. A number of algorithms involving compression techniques have thus been presented, to represent Web graphs succinctly but also providing random access. Those techniques are usually based on differential encodings of the adjacency lists, finding repeating nodes or node regions in the successive lists, more general grammar-based transformations or 2-dimensional representations of the binary matrix of the graph. In this paper we present two Web graph compression algorithms. The first can be seen as engineering of the Boldi and Vigna (2004) method. We extend the notion of similarity between link lists, and use a more compact encoding of residuals. The algorithm works on blocks of varying size (in the number of input lines) and sacrifices access time for better compression ratio, achieving more succinct graph representation than other algorithms reported in the literature. The second algorithm works on blocks of the same size, in the number of input lines, and its key mechanism is merging the block into a single ordered list. This method achieves much more attractive space-time tradeoffs.Comment: 15 page

Scene Graph Lossless Compression with Adaptive Prediction for Objects and Relations

The scene graph is a new data structure describing objects and their pairwise relationship within image scenes. As the size of scene graph in vision applications grows, how to losslessly and efficiently store such data on disks or transmit over the network becomes an inevitable problem. However, the compression of scene graph is seldom studied before because of the complicated data structures and distributions. Existing solutions usually involve general-purpose compressors or graph structure compression methods, which is weak at reducing redundancy for scene graph data. This paper introduces a new lossless compression framework with adaptive predictors for joint compression of objects and relations in scene graph data. The proposed framework consists of a unified prior extractor and specialized element predictors to adapt for different data elements. Furthermore, to exploit the context information within and between graph elements, Graph Context Convolution is proposed to support different graph context modeling schemes for different graph elements. Finally, a learned distribution model is devised to predict numerical data under complicated conditional constraints. Experiments conducted on labeled or generated scene graphs proves the effectiveness of the proposed framework in scene graph lossless compression task

VoG: Summarizing and Understanding Large Graphs

How can we succinctly describe a million-node graph with a few simple sentences? How can we measure the "importance" of a set of discovered subgraphs in a large graph? These are exactly the problems we focus on. Our main ideas are to construct a "vocabulary" of subgraph-types that often occur in real graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the most succinct description of a graph in terms of this vocabulary. We measure success in a well-founded way by means of the Minimum Description Length (MDL) principle: a subgraph is included in the summary if it decreases the total description length of the graph. Our contributions are three-fold: (a) formulation: we provide a principled encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop \method, an efficient method to minimize the description cost, and (c) applicability: we report experimental results on multi-million-edge real graphs, including Flickr and the Notre Dame web graph.Comment: SIAM International Conference on Data Mining (SDM) 201

The Limits of Popularity-Based Recommendations, and the Role of Social Ties

In this paper we introduce a mathematical model that captures some of the salient features of recommender systems that are based on popularity and that try to exploit social ties among the users. We show that, under very general conditions, the market always converges to a steady state, for which we are able to give an explicit form. Thanks to this we can tell rather precisely how much a market is altered by a recommendation system, and determine the power of users to influence others. Our theoretical results are complemented by experiments with real world social networks showing that social graphs prevent large market distortions in spite of the presence of highly influential users.Comment: 10 pages, 9 figures, KDD 201