117,872 research outputs found
Satcha Pretto
No full textSatcha Pretto uses her hands to add emphasis to her words. Behind her the Univision 23 logo is visible
Local computation of PageRank: The ranking side
No full textImagine you are a social network user who wants to search, in a list of potential candidates, for the best candidate for a job on the basis of their PageRank-induced importance ranking. Is it possible to compute this ranking for a low cost, by visiting only small subnetworks around the nodes that represent each candidate? The fundamental problem underpinning this question, i.e. computing locally the PageRank ranking of k nodes in an -node graph, was first raised by Chen et al. (CIKM 2004) and then restated by Bar-Yossef and Mashiach (CIKM 2008). In this paper we formalize and provide the first analysis of the problem, proving that any local algorithm that computes a correct ranking must take into consideration Ω(√(kn)) nodes - even when ranking the top nodes of the graph, even if their PageRank scores are "well separated", and even if the algorithm is randomized (and we prove a stronger Ω(n) bound for deterministic algorithms). Experiments carried out on large, publicly available crawls of the web and of a social network show that also in practice the fraction of the graph to be visited to compute the ranking may be considerable, both for algorithms that are always correct and for algorithms that employ (efficient) local score approximations
Etoiles - Giampaolo Pretto dirige l' Orchestra Filarmonica di Torino. Chloë Hanslip, violino
No full textGiampaolo Pretto, direttoreChloë Hanslip, violin
On Approximating the Stationary Distribution of Time-reversible Markov Chains
No full textApproximating the stationary probability of a state in a Markov chain through Markov chain Monte Carlo techniques is, in general, inefficient. Standard random walk approaches require tilde{O}(tau/pi(v)) operations to approximate the probability pi(v) of a state v in a chain with mixing time tau, and even the best available techniques still have complexity tilde{O}(tau^1.5 / pi(v)^0.5); and since these complexities depend inversely on pi(v), they can grow beyond any bound in the size of the chain or in its mixing time.
In this paper we show that, for time-reversible Markov chains, there exists a simple randomized approximation algorithm that breaks this "small-pi(v) barrier"
Brief announcement: On approximating pageRank locally with sublinear query complexity
No full textCan one compute the pageRank score of a single, arbitrary node in a graph, exploring only a vanishing fraction of the graph? We provide a positive answer to this extensively researched open question. We develop the first algorithm that, for any n-node graph, returns a multiplicative (1±ε)-approximation of the score of any given node with probability (1−δ), using at most On2/3 ln(n)1/3 ln(1/δ)2/3ε−2/3 = Õ(n2/3) queries which return either a node chosen uniformly at random, or the list of neighbours of a given node. Alternatively, we show that the same guarantees can be attained by fetching at most OE4/5d−3/5 ln(n)1/5 ln(1/δ)3/5ε−6/5 = Õ(E4/5) arcs, where E is the total number of arcs in the graph and d is its average degree
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