6,994 research outputs found
Adiabatic quantum algorithm for search engine ranking
We propose an adiabatic quantum algorithm for generating a quantum pure state
encoding of the PageRank vector, the most widely used tool in ranking the
relative importance of internet pages. We present extensive numerical
simulations which provide evidence that this algorithm can prepare the quantum
PageRank state in a time which, on average, scales polylogarithmically in the
number of webpages. We argue that the main topological feature of the
underlying web graph allowing for such a scaling is the out-degree
distribution. The top ranked entries of the quantum PageRank state
can then be estimated with a polynomial quantum speedup. Moreover, the quantum
PageRank state can be used in "q-sampling" protocols for testing properties of
distributions, which require exponentially fewer measurements than all
classical schemes designed for the same task. This can be used to decide
whether to run a classical update of the PageRank.Comment: 7 pages, 5 figures; closer to published versio
Investigating the Impact of the Blogsphere: Using PageRank to Determine the Distribution of Attention
Much has been written in recent years about the blogosphere and its impact on political, educational and scientific debates. Lately the issue has received significant attention from the industry. As the blogosphere continues to grow, even doubling its size every six months, this paper investigates its apparent impact on the overall Web itself. We use the popular Google PageRank algorithm which employs a model of Web used to measure the distribution of user attention across sites in the blogosphere. The paper is based on an analysis of the PageRank distribution for 8.8 million blogs in 2005 and 2006. This paper addresses the following key questions: How is PageRank distributed across the blogosphere? Does it indicate the existence of measurable, visible effects of blogs on the overall mediasphere? Can we compare the distribution of attention to blogs as characterised by the PageRank with the situation for other forms of Web content? Has there been a growth in the impact of the blogosphere on the Web over the two years analysed here? Finally, it will also be necessary to examine the limitations of a PageRank-centred approach
Ranking Spaces for Predicting Human Movement in an Urban Environment
A city can be topologically represented as a connectivity graph, consisting
of nodes representing individual spaces and links if the corresponding spaces
are intersected. It turns out in the space syntax literature that some defined
topological metrics can capture human movement rates in individual spaces. In
other words, the topological metrics are significantly correlated to human
movement rates, and individual spaces can be ranked by the metrics for
predicting human movement. However, this correlation has never been well
justified. In this paper, we study the same issue by applying the weighted
PageRank algorithm to the connectivity graph or space-space topology for
ranking the individual spaces, and find surprisingly that (1) the PageRank
scores are better correlated to human movement rates than the space syntax
metrics, and (2) the underlying space-space topology demonstrates small world
and scale free properties. The findings provide a novel justification as to why
space syntax, or topological analysis in general, can be used to predict human
movement. We further conjecture that this kind of analysis is no more than
predicting a drunkard's walking on a small world and scale free network.
Keywords: Space syntax, topological analysis of networks, small world, scale
free, human movement, and PageRankComment: 11 pages, 5 figures, and 2 tables, English corrections from version 1
to version 2, major changes in the section of introduction from version 2 to
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