Abstract. 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. 1.

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.

Extractors and taggers turn unstructured text into entityrelation (ER) graphs where nodes are entities (email, paper, person, conference, company) and edges are relations (wrote, cited, works-for). Typed proximity search of the form type=person NEAR company∼"IBM", paper∼"XML " is an increasingly useful search paradigm in ER graphs. Proximity search implementations either perform a Pagerank-like computation at query time, which is slow, or precompute, store and combine per-word Pageranks, which can be very expensive in terms of preprocessing time and space. We present HubRank, a new system for fast, dynamic, spaceefficient proximity searches in ER graphs. During preprocessing, HubRank computes and indexes certain “sketchy” random walk fingerprints for a small fraction of nodes, carefully chosen using query log statistics. At query time, a small “active ” subgraph is identified, bordered by nodes with indexed fingerprints. These fingerprints are adaptively loaded to various resolutions to form approximate personalized Pagerank vectors (PPVs). PPVs at remaining active nodes are now computed iteratively. We report on experiments with CiteSeer’s ER graph and millions of real Cite-Seer queries. Some representative numbers follow. On our testbed, HubRank preprocesses and indexes 52 times faster than whole-vocabulary PPV computation. A text index occupies 56 MB. Whole-vocabulary PPVs would consume 102 GB. If PPVs are truncated to 56 MB, precision compared to true Pagerank drops to 0.55; in contrast, HubRank has precision 0.91 at 63 MB. HubRank’s average query time is 200–300 milliseconds; query-time Pagerank computation takes 11 seconds on average.

The key factors for the success of the World Wide Web are its large size and the lack of a centralized control over its contents. Both issues are also the most important source of problems for locating information. The Web is a context in which traditional Information Retrieval methods are challenged, and given the volume of the Web and its speed of change, the coverage of modern search engines is relatively small. Moreover, the distribution of quality is very skewed, and interesting pages are scarce in comparison with the rest of the content. Web crawling is the process used by search engines to collect pages from the Web. This thesis studies Web crawling at several different levels, ranging from the long-term goal of crawling important pages first, to the short-term goal of using the network connectivity efficiently, including implementation issues that are essential for crawling in practice. We start by designing a new model and architecture for a Web crawler that tightly integrates the crawler with the rest of the search engine, providing access to the metadata and links of the documents that can be used to guide the crawling process effectively. We implement this design in the WIRE project as an efficient Web crawler that provides an experimental framework for this research. In fact, we have used our crawler to

The Google search engine uses a method called PageRank, together with term-based and other ranking techniques, to order search results returned to the user. PageRank uses link analysis to assign a global importance score to each web page. The PageRank scores of all the pages are usually determined off-line in a large-scale computation on the entire hyperlink graph of the web, and several recent studies have focused on improving the efficiency of this computation, which may require multiple hours on a typical workstation. However, in some scenarios, such as online analysis of link evolution and mining of large web archives, it may be desirable to quickly approximate or update the PageRanks of individual nodes without performing a large-scale computation on the entire graph. We address this problem by studying several methods for efficiently estimating the PageRank score of a particular web page using only a small subgraph of the entire web.

PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as a frequency of visiting a Web page by a random surfer and thus it reflects the popularity of a Web page. Google computes the PageRank using the power iteration method which requires about one week of intensive computations.

PageRank-style (PR) link analyses are a cornerstone of Web search engines and Web mining, but they are computationally expensive. Recently, various techniques have been proposed for speeding up these analyses by distributing the link graph among multiple sites. However, none of these advanced methods is suitable for a fully decentralized PR computation in a peer-to-peer (P2P) network with autonomous peers, where each peer can independently crawl Web fragments according to the user’s thematic interests. In such a setting the graph fragments that different peers have locally available or know about may arbitrarily overlap among peers, creating additional complexity for the PR computation. This paper presents the JXP algorithm for dynamically and collaboratively computing PR scores of Web pages that are arbitrarily distributed in a P2P network. The algorithm runs at every peer, and it works by combining locally computed PR scores with random meetings among the peers in the network. It is scalable as the number of peers on the network grows, and experiments as well as theoretical arguments show that JXP scores converge to the true PR scores that one would obtain by a centralized computation. 1.

Deciding which kind of visit accumulates high-quality pages more quickly is one of the most often debated issue in the design of web crawlers. It is known that breadth-first visits work well, as they tend to discover pages with high PageRank early on in the crawl. Indeed, this visit order is much better than depth first, which is in turn even worse than a random visit; nevertheless, breadth-first can be superseded using an omniscient visit that chooses, at every step, the node of highest PageRank in the frontier. This paper discusses a related, and previously overlooked, measure of effectivity for crawl strategies: whether the graph obtained after a partial visit is in some sense representative of the underlying web graph as far as the computation of PageRank is concerned. More precisely, we are interested in determining how rapidly the computation of PageRank over the visited subgraph yields relative ranks that agree with the ones the nodes have in the complete graph; ranks are compared using Kendall’s τ. We describe a number of large-scale experiments that show the following paradoxical effect: visits that gather PageRank more quickly (e.g., highest-quality-first) are also those that tend to miscalculate PageRank. Finally, we perform the same kind of experimental analysis on some synthetic random graphs, generated using well-known web-graph models: the results are almost opposite to those obtained on real web graphs. 1

A fundamental consideration in designing successful trust scores in a peer-to-peer system is the self-interest of individual peers. We propose a strategyproof partition mechanism that provides incentives for peers to share files, is non-manipulable by selfish interests, and approximates trust scores based on EigenTrust[5]. The basic idea behind the partition mechanism is that the peers are partitioned into peer groups and incentives are structured so that a peer only downloads from peers in one particular peer group. When peers are myopic, we show that the total error in the trust values decreases exponentially with the number of peer groups, but when peers plan for the future, the total error decreases linearly with the number of peer groups. There is a direct tradeoff here between approximating EigenTrust well and keeping the trust values we are approximating useful.

Abstract. We introduce a novel bookmark-coloring algorithm (BCA) that computes authority weights over the web pages utilizing the web hyperlink structure. The computed vector (BCV) is similar to the PageRank vector defined for a page-specific teleportation. Meanwhile, BCA is very fast, and BCV is sparse. BCA also has important algebraic properties. If several BCVs corresponding to a set of pages (called hub) areknown,they can be leveraged in computing arbitrary BCV via a straightforward algebraic process and hub BCVs can be efficiently computed and encoded. 1.