To exploit the similarity information hidden in the hyperlink structure of the Web, this paper introduces algorithms scalable to graphs with billions of vertices on a distributed architecture. The similarity of multistep neighborhoods of vertices are numerically evaluated by similarity functions including SimRank, a recursive refinement of cocitation, and PSimRank, a novel variant with better theoretical characteristics. Our methods are presented in a general framework of Monte Carlo similarity search algorithms that precompute an index database of random fingerprints, and at query time, similarities are estimated from the fingerprints. We justify our approximation method by asymptotic worst-case lower bounds: we show that there is a significant gap between exact and approximate approaches, and suggest that the exact computation, in general, is infeasible for large-scale inputs. We were the first to evaluate SimRank on real Web data. On the Stanford WebBase graph of 80M pages the quality of the methods increased significantly in each refinement step until step four

Personalized PageRank expresses link-based page quality around user selected pages. The only previous personalized PageRank algorithm that can serve on-line queries for an unrestricted choice of pages on large graphs is our Monte Carlo algorithm [WAW 2004]. In this paper we achieve unrestricted personalization by combining rounding and randomized sketching techniques in the dynamic programming algorithm of Jeh and Widom [WWW 2003]. We evaluate the precision of approximation experimentally on large scale real-world data and find significant improvement over previous results. As a key theoretical contribution we show that our algorithms use an optimal amount of space by also improving earlier asymptotic worst-case lower bounds. Our lower bounds and algorithms apply to the SimRank as well; of independent interest is the reduction of the SimRank computation to personalized PageRank.

To exploit the similarity information hidden in the hyperlink structure of the web, this paper introduces algorithms scalable to graphs with billions of vertices on a distributed architecture. The similarity of multi-step neighborhoods of vertices are numerically evaluated by similarity functions including SimRank [20], a recursive refinement of cocitation; PSimRank, a novel variant with better theoretical characteristics; and the Jaccard coefficient, extended to multi-step neighborhoods. Our methods are presented in a general framework of Monte Carlo similarity search algorithms that precompute an index database of random fingerprints, and at query time, similarities are estimated from the fingerprints. The performance and quality of the methods were tested on the Stanford Webbase [19] graph of 80M pages by comparing our scores to similarities extracted from the ODP directory [26]. Our experimental results suggest that the hyperlink structure of vertices within four to five steps provide more adequate information for similarity search than single-step neighborhoods.

Today there is an emerging demand of Internet and network related service to collect the valuable service usage data and process it using data mining methods. In this paper, a generalized scheme for preprocessing and high-density compression of log files is presented. The aim of the method is to provide a base for long-term storage in a form appropriate for direct processing by data mining algorithms. Experiments on real log data show that the differentiated semantic log compression (dslc) methods compress at 2-3%, outperforming general-purpose compression utilities. This paper also demonstrates the flexibility of the pipeline concept by inlaying a field-wise compression algorithm to improve the compression efficiency. The implementation of this scheme was designed for the largest Hungarian Internet content provider.