arXiv subjects

Sebastiano Vigna

Publications and source records attributed to Sebastiano Vigna.

At least 37 records · Page 2Linked to original sources

arXiv2016

Efficient Optimally Lazy Algorithms for Minimal-Interval Semantics

Minimal-interval semantics associates with each query over a document a set of intervals, called witnesses, that are incomparable with respect to inclusion (i.e., they form an antichain): witnesses define the minimal regions of the document satisfying the query. Minimal-interval semantics makes it easy to define and compute several sophisticated proximity operators, provides snippets for user presentation, and can be used to rank documents. In this paper we provide algorithms for computing conjunction and disjunction that are linear in the number of intervals and logarithmic in the number of operands; for additional operators, such as ordered conjunction and Brouwerian difference, we provide linear algorithms. In all cases, space is linear in the number of operands. More importantly, we define a formal notion of optimal laziness, and either prove it, or prove its impossibility, for each algorithm. We cast our results in a general framework of antichains of intervals on total orders, making our algorithms directly applicable to other domains.

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arXiv2016

Further scramblings of Marsaglia's xorshift generators

xorshift* generators are a variant of Marsaglia's xorshift generators that eliminate linear artifacts typical of generators based on $\mathbf Z/2\mathbf Z$-linear operations using multiplication by a suitable constant. Shortly after high-dimensional xorshift* generators were introduced, Saito and Matsumoto suggested a different way to eliminate linear artifacts based on addition in $\mathbf Z/2^{32}\mathbf Z$, leading to the XSadd generator. Starting from the observation that the lower bits of XSadd are very weak, as its reverse fails systematically several statistical tests, we explore xorshift+, a variant of XSadd using 64-bit operations, which leads, in small dimension, to extremely fast high-quality generators.

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arXiv2016

Fast Scalable Construction of (Minimal Perfect Hash) Functions

Recent advances in random linear systems on finite fields have paved the way for the construction of constant-time data structures representing static functions and minimal perfect hash functions using less space with respect to existing techniques. The main obstruction for any practical application of these results is the cubic-time Gaussian elimination required to solve these linear systems: despite they can be made very small, the computation is still too slow to be feasible. In this paper we describe in detail a number of heuristics and programming techniques to speed up the resolution of these systems by several orders of magnitude, making the overall construction competitive with the standard and widely used MWHC technique, which is based on hypergraph peeling. In particular, we introduce broadword programming techniques for fast equation manipulation and a lazy Gaussian elimination algorithm. We also describe a number of technical improvements to the data structure which further reduce space usage and improve lookup speed. Our implementation of these techniques yields a minimal perfect hash function data structure occupying 2.24 bits per element, compared to 2.68 for MWHC-based ones, and a static function data structure which reduces the multiplicative overhead from 1.23 to 1.03.

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arXiv2016

BUbiNG: Massive Crawling for the Masses

Although web crawlers have been around for twenty years by now, there is virtually no freely available, opensource 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 paper aims at filling this gap, through the description of BUbiNG, our next-generation web crawler built upon the authors' experience with UbiCrawler [Boldi et al. 2004] and on the last ten years of research on the topic. BUbiNG is an opensource Java fully distributed crawler; a single BUbiNG agent, using sizeable hardware, can crawl several thousands 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 so to achieve very high throughput.

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arXiv2015

Liquid FM: Recommending Music through Viscous Democracy

Most modern recommendation systems use the approach of collaborative filtering: users that are believed to behave alike are used to produce recommendations. In this work we describe an application (Liquid FM) taking a completely different approach. Liquid FM is a music recommendation system that makes the user responsible for the recommended items. Suggestions are the result of a voting scheme, employing the idea of viscous democracy. Liquid FM can also be thought of as the first testbed for this voting system. In this paper we outline the design and architecture of the application, both from the theoretical and from the implementation viewpoints.

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arXiv2014

Interactions of cultures and top people of Wikipedia from ranking of 24 language editions

Wikipedia is a huge global repository of human knowledge, that can be leveraged to investigate interwinements between cultures. With this aim, we apply methods of Markov chains and Google matrix, for the analysis of the hyperlink networks of 24 Wikipedia language editions, and rank all their articles by PageRank, 2DRank and CheiRank algorithms. Using automatic extraction of people names, we obtain the top 100 historical figures, for each edition and for each algorithm. We investigate their spatial, temporal, and gender distributions in dependence of their cultural origins. Our study demonstrates not only the existence of skewness with local figures, mainly recognized only in their own cultures, but also the existence of global historical figures appearing in a large number of editions. By determining the birth time and place of these persons, we perform an analysis of the evolution of such figures through 35 centuries of human history for each language, thus recovering interactions and entanglement of cultures over time. We also obtain the distributions of historical figures over world countries, highlighting geographical aspects of cross-cultural links. Considering historical figures who appear in multiple editions as interactions between cultures, we construct a network of cultures and identify the most influential cultures according to this network.

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arXiv2014

A Weighted Correlation Index for Rankings with Ties

Understanding the correlation between two different scores for the same set of items is a common problem in information retrieval, and the most commonly used statistics that quantifies this correlation is Kendall's $τ$. 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 while comparing centrality scores on large graphs, as the obvious baseline, indegree, has a very large number of ties in web and social 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.

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arXiv2014

Supremum-Norm Convergence for Step-Asynchronous Successive Overrelaxation on M-matrices

Step-asynchronous successive overrelaxation updates the values contained in a single vector using the usual Gauß-Seidel-like weighted rule, but arbitrarily mixing old and new values, the only constraint being temporal coherence: you cannot use a value before it has been computed. We show that given a nonnegative real matrix $A$, a $σ\geqρ(A)$ and a vector $\boldsymbol w>0$ such that $A\boldsymbol w\leqσ\boldsymbol w$, every iteration of step-asynchronous successive overrelaxation for the problem $(sI- A)\boldsymbol x=\boldsymbol b$, with $s >σ$, reduces geometrically the $\boldsymbol w$-norm of the current error by a factor that we can compute explicitly. Then, we show that given a $σ>ρ(A)$ it is in principle always possible to compute such a $\boldsymbol w$. This property makes it possible to estimate the supremum norm of the absolute error at each iteration without any additional hypothesis on $A$, even when $A$ is so large that computing the product $A\boldsymbol x$ is feasible, but estimating the supremum norm of $(sI-A)^{-1}$ is not.

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arXiv2014

Fibonacci Binning

This note argues that when dot-plotting distributions typically found in papers about web and social networks (degree distributions, component-size distributions, etc.), and more generally distributions that have high variability in their tail, an exponentially binned version should always be plotted, too, and suggests Fibonacci binning as a visually appealing, easy-to-use and practical choice.

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arXiv2013

Cache-Oblivious Peeling of Random Hypergraphs

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 $O(\mathrm{sort}(n))$ 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.

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arXiv2013

Axioms for Centrality

Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were proposed to account for the importance of the nodes of a network. In this paper, we try to provide a mathematically sound survey of the most important classic centrality measures known from the literature and propose an axiomatic approach to establish whether they are actually doing what they have been designed for. Our axioms suggest some simple, basic properties that a centrality measure should exhibit. Surprisingly, only a new simple measure based on distances, harmonic centrality, turns out to satisfy all axioms; essentially, harmonic centrality is a correction to Bavelas's classic closeness centrality designed to take unreachable nodes into account in a natural way. As a sanity check, we examine in turn each measure under the lens of information retrieval, leveraging state-of-the-art knowledge in the discipline to measure the effectiveness of the various indices in locating web pages that are relevant to a query. While there are some examples of this comparisons in the literature, here for the first time we take into consideration centrality measures based on distances, such as closeness, in an information-retrieval setting. The results match closely the data we gathered using our axiomatic approach. Our results suggest that centrality measures based on distances, which have been neglected in information retrieval in favour of spectral centrality measures in the last years, are actually of very high quality; moreover, harmonic centrality pops up as an excellent general-purpose centrality index for arbitrary directed graphs.

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arXiv2013

In-Core Computation of Geometric Centralities with HyperBall: A Hundred Billion Nodes and Beyond

Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were proposed to account for the importance of the nodes of a network. In this paper, we approach the problem of computing geometric centralities, such as closeness and harmonic centrality, on very large graphs; traditionally this task requires an all-pairs shortest-path computation in the exact case, or a number of breadth-first traversals for approximated computations, but these techniques yield very weak statistical guarantees on highly disconnected graphs. We rather assume that the graph is accessed in a semi-streaming fashion, that is, that adjacency lists are scanned almost sequentially, and that a very small amount of memory (in the order of a dozen bytes) per node is available in core memory. We leverage the newly discovered algorithms based on HyperLogLog counters, making it possible to approximate a number of geometric centralities at a very high speed and with high accuracy. While the application of similar algorithms for the approximation of closeness was attempted in the MapReduce framework, our exploitation of HyperLogLog counters reduces exponentially the memory footprint, paving the way for in-core processing of networks with a hundred billion nodes using "just" 2TiB of RAM. Moreover, the computations we describe are inherently parallelizable, and scale linearly with the number of available cores.

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arXiv2013

Broadword Implementation of Parenthesis Queries

We continue the line of research started in "Broadword Implementation of Rank/Select Queries" proposing broadword (a.k.a. SWAR, "SIMD Within A Register") algorithms for finding matching closed parentheses and the k-th far closed parenthesis. Our algorithms work in time O(log w) on a word of w bits, and contain no branch and no test instruction. On 64-bit (and wider) architectures, these algorithms make it possible to avoid costly tabulations, while providing a very significant speedup with respect to for-loop implementations.

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arXiv2012

Predecessor search with distance-sensitive query time

A predecessor (successor) search finds the largest element $x^-$ smaller than the input string $x$ (the smallest element $x^+$ larger than or equal to $x$, respectively) out of a given set $S$; in this paper, we consider the static case (i.e., $S$ is fixed and does not change over time) and assume that the $n$ elements of $S$ are available for inspection. We present a number of algorithms that, with a small additional index (usually of O(n log w) bits, where $w$ is the string length), can answer predecessor/successor queries quickly and with time bounds that depend on different kinds of distance, improving significantly several results that appeared in the recent literature. Intuitively, our first result has a running time that depends on the distance between $x$ and $x^\pm$: it is especially efficient when the input $x$ is either very close to or very far from $x^-$ or $x^+$; our second result depends on some global notion of distance in the set $S$, and is fast when the elements of $S$ are more or less equally spaced in the universe; finally, for our third result we rely on a finger (i.e., an element of $S$) to improve upon the first one; its running time depends on the distance between the input and the finger.

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arXiv2012

Quasi-Succinct Indices

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 and, in practice, significant performance improvements on conjunctive, phrasal and proximity queries.

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arXiv2012

Four Degrees of Separation, Really

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.

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arXiv2012

Four Degrees of Separation

Frigyes Karinthy, in his 1929 short story "Láancszemek" ("Chains") suggested that any two persons are distanced by at most six friendship links. (The exact wording of the story is slightly ambiguous: "He bet us that, using no more than five individuals, one of whom is a personal acquaintance, he could contact the selected individual [...]". It is not completely clear whether the selected individual is part of the five, so this could actually allude to distance five or six in the language of graph theory, but the "six degrees of separation" phrase stuck after John Guare's 1990 eponymous play. Following Milgram's definition and Guare's interpretation, we will assume that "degrees of separation" is the same as "distance minus one", where "distance" is the usual path length-the number of arcs in the path.) Stanley Milgram in his famous experiment challenged people to route postcards to a fixed recipient by passing them only through direct acquaintances. The average number of intermediaries on the path of the postcards lay between 4.4 and 5.7, depending on the sample of people chosen. We report the results of the first world-scale social-network graph-distance computations, using the entire Facebook network of active users (\approx721 million users, \approx69 billion friendship links). The average distance we observe is 4.74, corresponding to 3.74 intermediaries or "degrees of separation", showing that the world is even smaller than we expected, and prompting the title of this paper. More generally, we study the distance distribution of Facebook and of some interesting geographic subgraphs, looking also at their evolution over time. The networks we are able to explore are almost two orders of magnitude larger than those analysed in the previous literature. We report detailed statistical metadata showing that our measurements (which rely on probabilistic algorithms) are very accurate.

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arXiv2011

Robustness of Social Networks: Comparative Results Based on Distance Distributions

Given a social network, which of its nodes have a stronger impact in determining its structure? More formally: which node-removal order has the greatest impact on the network structure? We approach this well-known problem for the first time in a setting that combines both web graphs and social networks, using datasets that are orders of magnitude larger than those appearing in the previous literature, thanks to some recently developed algorithms and software tools that make it possible to approximate accurately the number of reachable pairs and the distribution of distances in a graph. Our experiments highlight deep differences in the structure of social networks and web graphs, show significant limitations of previous experimental results, and at the same time reveal clustering by label propagation as a new and very effective way of locating nodes that are important from a structural viewpoint.

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