3,478 research outputs found
Fast Distributed PageRank Computation
Over the last decade, PageRank has gained importance in a wide range of
applications and domains, ever since it first proved to be effective in
determining node importance in large graphs (and was a pioneering idea behind
Google's search engine). In distributed computing alone, PageRank vector, or
more generally random walk based quantities have been used for several
different applications ranging from determining important nodes, load
balancing, search, and identifying connectivity structures. Surprisingly,
however, there has been little work towards designing provably efficient
fully-distributed algorithms for computing PageRank. The difficulty is that
traditional matrix-vector multiplication style iterative methods may not always
adapt well to the distributed setting owing to communication bandwidth
restrictions and convergence rates.
In this paper, we present fast random walk-based distributed algorithms for
computing PageRanks in general graphs and prove strong bounds on the round
complexity. We first present a distributed algorithm that takes O\big(\log
n/\eps \big) rounds with high probability on any graph (directed or
undirected), where is the network size and \eps is the reset probability
used in the PageRank computation (typically \eps is a fixed constant). We
then present a faster algorithm that takes O\big(\sqrt{\log n}/\eps \big)
rounds in undirected graphs. Both of the above algorithms are scalable, as each
node sends only small (\polylog n) number of bits over each edge per round.
To the best of our knowledge, these are the first fully distributed algorithms
for computing PageRank vector with provably efficient running time.Comment: 14 page
Bidirectional PageRank Estimation: From Average-Case to Worst-Case
We present a new algorithm for estimating the Personalized PageRank (PPR)
between a source and target node on undirected graphs, with sublinear
running-time guarantees over the worst-case choice of source and target nodes.
Our work builds on a recent line of work on bidirectional estimators for PPR,
which obtained sublinear running-time guarantees but in an average-case sense,
for a uniformly random choice of target node. Crucially, we show how the
reversibility of random walks on undirected networks can be exploited to
convert average-case to worst-case guarantees. While past bidirectional methods
combine forward random walks with reverse local pushes, our algorithm combines
forward local pushes with reverse random walks. We also discuss how to modify
our methods to estimate random-walk probabilities for any length distribution,
thereby obtaining fast algorithms for estimating general graph diffusions,
including the heat kernel, on undirected networks.Comment: Workshop on Algorithms and Models for the Web-Graph (WAW) 201
A Note on the PageRank of Undirected Graphs
The PageRank is a widely used scoring function of networks in general and of
the World Wide Web graph in particular. The PageRank is defined for directed
graphs, but in some special cases applications for undirected graphs occur. In
the literature it is widely noted that the PageRank for undirected graphs are
proportional to the degrees of the vertices of the graph. We prove that
statement for a particular personalization vector in the definition of the
PageRank, and we also show that in general, the PageRank of an undirected graph
is not exactly proportional to the degree distribution of the graph: our main
theorem gives an upper and a lower bound to the L_1 norm of the difference of
the PageRank and the degree distribution vectors
Personalized PageRank with Node-dependent Restart
Personalized PageRank is an algorithm to classify the improtance of web pages
on a user-dependent basis. We introduce two generalizations of Personalized
PageRank with node-dependent restart. The first generalization is based on the
proportion of visits to nodes before the restart, whereas the second
generalization is based on the probability of visited node just before the
restart. In the original case of constant restart probability, the two measures
coincide. We discuss interesting particular cases of restart probabilities and
restart distributions. We show that the both generalizations of Personalized
PageRank have an elegant expression connecting the so-called direct and reverse
Personalized PageRanks that yield a symmetry property of these Personalized
PageRanks
- …