11,777 research outputs found
Estimating and Sampling Graphs with Multidimensional Random Walks
Estimating characteristics of large graphs via sampling is a vital part of
the study of complex networks. Current sampling methods such as (independent)
random vertex and random walks are useful but have drawbacks. Random vertex
sampling may require too many resources (time, bandwidth, or money). Random
walks, which normally require fewer resources per sample, can suffer from large
estimation errors in the presence of disconnected or loosely connected graphs.
In this work we propose a new -dimensional random walk that uses
dependent random walkers. We show that the proposed sampling method, which we
call Frontier sampling, exhibits all of the nice sampling properties of a
regular random walk. At the same time, our simulations over large real world
graphs show that, in the presence of disconnected or loosely connected
components, Frontier sampling exhibits lower estimation errors than regular
random walks. We also show that Frontier sampling is more suitable than random
vertex sampling to sample the tail of the degree distribution of the graph
Provable and practical approximations for the degree distribution using sublinear graph samples
The degree distribution is one of the most fundamental properties used in the
analysis of massive graphs. There is a large literature on graph sampling,
where the goal is to estimate properties (especially the degree distribution)
of a large graph through a small, random sample. The degree distribution
estimation poses a significant challenge, due to its heavy-tailed nature and
the large variance in degrees.
We design a new algorithm, SADDLES, for this problem, using recent
mathematical techniques from the field of sublinear algorithms. The SADDLES
algorithm gives provably accurate outputs for all values of the degree
distribution. For the analysis, we define two fatness measures of the degree
distribution, called the -index and the -index. We prove that SADDLES is
sublinear in the graph size when these indices are large. A corollary of this
result is a provably sublinear algorithm for any degree distribution bounded
below by a power law.
We deploy our new algorithm on a variety of real datasets and demonstrate its
excellent empirical behavior. In all instances, we get extremely accurate
approximations for all values in the degree distribution by observing at most
of the vertices. This is a major improvement over the state-of-the-art
sampling algorithms, which typically sample more than of the vertices to
give comparable results. We also observe that the and -indices of real
graphs are large, validating our theoretical analysis.Comment: Longer version of the WWW 2018 submissio
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