Progress in High-Performance Computing in general, and High-Performance Graph Processing in particular, is highly dependent on the availability of publicly-accessible, relevant, and realistic data sets. To ensure continuation of this progress, we (i) investigate and optimize the process of generating large sequence similarity graphs as an HPC challenge and (ii) demonstrate this process in creating MS-BioGraphs, a new family of publicly available real-world edge-weighted graph datasets with up to 2.5 trillion edges, that is, 6.6 times greater than the largest graph published recently. The largest graph is created by matching (i.e., all-toall similarity aligning) 1.7 billion protein sequences. The MSBioGraphs family includes also seven subgraphs with different sizes and direction types. We describe two main challenges we faced in generating large graph datasets and our solutions, that are, (i) optimizing data structures and algorithms for this multi-step process and (ii) WebGraph parallel compression technique. The datasets are available online on https://blogs.qub.ac.uk/ DIPSA/MS-BioGraphs.

Recent advances in the compact representation of static functions (with constant access time) have made it possible to fully exploit constructions based on random linear system. Such constructions, albeit theoretically appealing, were previously too slow to be usable. In this paper, we extend such techniques to the problem of storing compressed static functions, in the sense that the space used per key should be close to the entropy of the list of values. From a theoretical viewpoint, we are inspired by the approach of Hreinsson, Krøyer and Pagh. Values are represented using a near-optimal instantaneous code. Then, a bit array is created so that by XOR'ing its content at a fixed number of positions depending on the key one obtains the value, represented by its associated codeword. In the construction phase, every bit of the array is associated with an equation on Z/2Z, and solving the associated system provides the desired representation. Thus, we pass from one equation per key (the non-compressed case) to one equation per bit: the size of the system is thus approximately multiplied by the empirical entropy of the values, making the problem much more challenging. We show that by carefully engineering the value representation we can obtain a practical data structure. For example, we can store a function with geometrically distributed output in just 2.28 bits per key, independently of the key set, with a construction time double with respect to that of a state-of-the-art non-compressed function, which requires ≈ log log n bits per key, where n is the number of keys, and slightly improved lookup time. We can also store a function with an output of 106 values distributed following a power law of exponent 2 in just 2.75 bits per key, whereas a non-compressed function would require more than 20, with a threefold increase in construction time and significantly faster lookups.

Although web crawlers have been around for twenty years by now, there is virtually no freely available, open-source crawling software that guarantees high throughput, overcomes the limits of single-machine systems, and, at the same time, scales linearly with the amount of resources available. This article aims at filling this gap, through the description of BUbiNG, our next-generation web crawler built upon the authors’ experience with UbiCrawler [9] and on the last ten years of research on the topic. BUbiNG is an open-source Java fully distributed crawler; a single BUbiNG agent, using sizeable hardware, can crawl several thousand pages per second respecting strict politeness constraints, both host- and IP-based. Unlike existing open-source distributed crawlers that rely on batch techniques (like MapReduce), BUbiNG job distribution is based on modern high-speed protocols to achieve very high throughput.

Understanding the correlation between two different scores for the same set of items is a common problem in graph analysis and information retrieval. The most commonly used statistics that quantifies this correlation is Kendall's tau; however, the standard definition fails to capture that discordances between items with high rank are more important than those between items with low rank. Recently, a new measure of correlation based on average precision has been proposed to solve this problem, but like many alternative proposals in the literature it assumes that there are no ties in the scores. This is a major deficiency in a number of contexts, and in particular when comparing centrality scores on large graphs, as the obvious baseline, indegree, has a very large number of ties in social networks and web graphs. We propose to extend Kendall's definition in a natural way to take into account weights in the presence of ties. We prove a number of interesting mathematical properties of our generalization and describe an O(n\log n) algorithm for its computation. We also validate the usefulness of our weighted measure of correlation using experimental data on social networks and web graphs.

The computation of a peeling order in a randomly generated hypergraph is the most time-consuming step in a number of constructions, such as perfect hashing schemes, random r-SAT solvers, error-correcting codes, and approximate set encodings. While there exists a straightforward linear-time algorithm, its poor I/O performance makes it impractical for hypergraphs whose size exceeds the available internal memory. We show how to reduce the computation of a peeling order to a small number of sequential scans and sorts, and analyze its I/O complexity in the cache-oblivious model. The resulting algorithm requires O.sort.n// I/Os and O.n log n/ time to peel a random hypergraph with n edges. We experimentally evaluate the performance of our implementation of this algorithm in a real-world scenario by using the construction of minimal perfect hash functions (MPHF) as our test case: our algorithm builds a MPHF of 7:6 billion keys in less than 21 hours on a single machine. The resulting data structure is both more space-efficient and faster than that obtained with the current state-of-the-art MPHF construction for large-scale key sets.

Compressed inverted indices in use today are based on the idea of gap compression: documents pointers are stored in increasing order, and the gaps between successive document pointers are stored using suitable codes which represent smaller gaps using less bits. Additional data such as counts and positions is stored using similar techniques. A large body of research has been built in the last 30 years around gap compression, including theoretical modeling of the gap distribution, specialized instantaneous codes suitable for gap encoding, and ad hoc document reorderings which increase the efficiency of instantaneous codes. This paper proposes to represent an index using a different architecture based on quasi-succinct representation of monotone sequences. We show that, besides being theoretically elegant and simple, the new index provides expected constant-time operations, space savings, and, in practice, significant performance improvements on conjunctive, phrasal and proximity queries.

We recently measured the average distance of users in the Facebook graph, spurring comments in the scientific community as well as in the general press ("Four Degrees of Separation"). A number of interesting criticisms have been made about the meaningfulness, methods and consequences of the experiment we performed. In this paper we want to discuss some methodological aspects that we deem important to underline in the form of answers to the questions we have read in newspapers, magazines, blogs, or heard from colleagues. We indulge in some reflections on the actual meaning of "average distance" and make a number of side observations showing that, yes, 3.74 "degrees of separation" are really few.

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.

The neighbourhood function NG(t) of a graph G gives, for each t ∈ N, the number of pairs of nodes x, y such that y is reachable from x in less that t hops. The neighbourhood function provides a wealth of information about the graph [10] (e.g., it easily allows one to compute its diameter), but it is very expensive to compute it exactly. Recently, the ANF algorithm [10] (approximate neighbourhood function) has been proposed with the purpose of approximating NG(t) on large graphs. We describe a breakthrough improvement over ANF in terms of speed and scalability. Our algorithm, called HyperANF, uses the new HyperLogLog counters [5] and combines them efficiently through broadword programming [8]; our implementation uses talk decomposition to exploit multi-core parallelism. With HyperANF, for the first time we can compute in a few hours the neighbourhood function of graphs with billions of nodes with a small error and good confidence using a standard workstation.

A voting system is a set of rules that a community adopts to take collective decisions. In this paper we study voting systems for a particular kind of community: electronically mediated social networks. In particular, we focus on delegative democracy (a.k.a. proxy voting) that has recently received increased interest for its ability to combine the benefits of direct and representative systems, and that seems also perfectly suited for electronically mediated social networks. In such a context, we consider a voting system in which users can only express their preference for one among the people they are explicitly connected with, and this preference can be propagated transitively, using an attenuation factor. We present this system and we study its properties. We also take into consideration the problem of missing votes, which is particularly relevant in online networks, as some recent case shows. Our experiments on real-world networks provide interesting insight into the significance and stability of the results obtained with the suggested voting system.

Understanding query reformulation patterns is a key step towards next generation web search engines: it can help improving users' web-search experience by predicting their intent, and thus helping them to locate information more effectively. As a step in this direction, we build an accurate model for classifying user query reformulations into broad classes (generalization, specialization, error correction or parallel move), achieving 92\% accuracy. We apply the model to automatically label two large query logs, creating annotated query-flow graphs. We study the resulting reformulation patterns, finding results consistent with previous studies done on smaller manually annotated datasets, and discovering new interesting patterns, including connections between reformulation types and topical categories. Finally, applying our findings to a third query log that is publicly available for research purposes, we demonstrate that our reformulation classifier leads to improved recommendations in a query recommendation system.

research-article Share on PageRank: Functional dependencies Authors: Paolo Boldi Università degli Studi di Milano, Milano, MI, Italy Università degli Studi di Milano, Milano, MI, ItalyView Profile , Massimo Santini Università degli Studi di Milano, Milano, MI, Italy Università degli Studi di Milano, Milano, MI, ItalyView Profile , Sebastiano Vigna Università degli Studi di Milano, Milano, MI, Italy Università degli Studi di Milano, Milano, MI, ItalyView Profile Authors Info & Claims ACM Transactions on Information SystemsVolume 27Issue 4Article No.: 19pp 1–23https://doi.org/10.1145/1629096.1629097Published:30 November 2009Publication History 71citation1,468DownloadsMetricsTotal Citations71Total Downloads1,468Last 12 Months42Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

Query logs record the queries and the actions of the users of engines, and as such they contain valuable information about the interests, the preferences, and the behavior of the users, as well as their implicit feedback to engine results. Mining the wealth of information available in the query logs has many important applications including query-log analysis, user profiling and personalization, advertising, query recommendation, and more.In this paper we introduce the query-flow graph, a graph representation of the interesting knowledge about latent querying behavior. Intuitively, in the query-flow graph a directed edge from query qi to query qj means that the two queries are likely to be part of the same search mission. Any path over the query-flow graph may be seen as a searching behavior, whose likelihood is given by the strength of the edges along the path.The query-flow graph is an outcome of query-log mining and, at the same time, a useful tool for it. We propose a methodology that builds such a graph by mining time and textual information as well as aggregating queries from different users. Using this approach we build a real-world query-flow graph from a large-scale query log and we demonstrate its utility in concrete applications, namely, finding logical sessions, and query recommendation. We believe, however, that the usefulness of the query-flow graph goes beyond these two applications.

PageRank is defined as the stationary state of a Markov chain. The chain is obtained by perturbing the transition matrix induced by a web graph with a damping factor α that spreads uniformly part of the rank. The choice of α is eminently empirical, and in most cases the original suggestion α = 0.85 by Brin and Page is still used. Recently, however, the behaviour of PageRank with respect to changes in α was discovered to be useful in link-spam detection[21]. Moreover, an analytical justification of the value chosen for α is still missing. In this paper, we give the first mathematical analysis of PageRank when α changes. In particular, we show that, contrarily to popular belief, for real-world graphs values of α close to 1 do not give a more meaningful ranking. Then, we give closed-form formulae for PageRank derivatives of any order, and an extension of the Power Method that approximates them with convergence O (tk αt) for the k-th derivative. Finally, we show a tight connection between iterated computation and analytical behaviour by proving that the k-th iteration of the Power Method gives exactly the PageRank value obtained using a Maclaurin polynomial of degree k. The latter result paves the way towards the application of analytical methods to the study of PageRank.

This paper describes the Web graph framework that provides simple methods to manage very large graphs, specially tailored around Web graphs. A fundamental observation about compression of the web graph was made in the construction of the LINK database. Web graph contains a fully-documented implementation of various instantaneous codes, and of parameterisable compression algorithms that achieve the best compression rates and introducing a new technique called intervalisation. Web graph also contains algorithms for accessing a compressed graph.

Studying web graphs is often difficult due to their large size. Recently,several proposals have been published about various techniques that allow tostore a web graph in memory in a limited space, exploiting the inner redundancies of the web. The WebGraph framework is a suite of codes, algorithms and tools that aims at making it easy to manipulate large web graphs. This papers presents the compression techniques used in WebGraph, which are centred around referentiation and intervalisation (which in turn are dual to each other). WebGraph can compress the WebBase graph (118 Mnodes, 1 Glinks)in as little as 3.08 bits per link, and its transposed version in as littleas 2.89 bits per link.