19,774 research outputs found
Faster Random Walks By Rewiring Online Social Networks On-The-Fly
Many online social networks feature restrictive web interfaces which only
allow the query of a user's local neighborhood through the interface. To enable
analytics over such an online social network through its restrictive web
interface, many recent efforts reuse the existing Markov Chain Monte Carlo
methods such as random walks to sample the social network and support analytics
based on the samples. The problem with such an approach, however, is the large
amount of queries often required (i.e., a long "mixing time") for a random walk
to reach a desired (stationary) sampling distribution.
In this paper, we consider a novel problem of enabling a faster random walk
over online social networks by "rewiring" the social network on-the-fly.
Specifically, we develop Modified TOpology (MTO)-Sampler which, by using only
information exposed by the restrictive web interface, constructs a "virtual"
overlay topology of the social network while performing a random walk, and
ensures that the random walk follows the modified overlay topology rather than
the original one. We show that MTO-Sampler not only provably enhances the
efficiency of sampling, but also achieves significant savings on query cost
over real-world online social networks such as Google Plus, Epinion etc.Comment: 15 pages, 14 figure, technical report for ICDE2013 paper. Appendix
has all the theorems' proofs; ICDE'201
Motif counting beyond five nodes
Counting graphlets is a well-studied problem in graph mining and social network analysis. Recently, several papers explored very simple and natural algorithms based on Monte Carlo sampling of Markov Chains (MC), and reported encouraging results. We show, perhaps surprisingly, that such algorithms are outperformed by color coding (CC) [2], a sophisticated algorithmic technique that we extend to the case of graphlet sampling and for which we prove strong statistical guarantees. Our computational experiments on graphs with millions of nodes show CC to be more accurate than MC; furthermore, we formally show that the mixing time of the MC approach is too high in general, even when the input graph has high conductance. All this comes at a price however. While MC is very efficient in terms of space, CCâs memory requirements become demanding when the size of the input graph and that of the graphlets grow. And yet, our experiments show that CC can push the limits of the state-of-the-art, both in terms of the size of the input graph and of that of the graphlets
A Cubic Algorithm for Computing Gaussian Volume
We present randomized algorithms for sampling the standard Gaussian
distribution restricted to a convex set and for estimating the Gaussian measure
of a convex set, in the general membership oracle model. The complexity of
integration is while the complexity of sampling is for
the first sample and for every subsequent sample. These bounds
improve on the corresponding state-of-the-art by a factor of . Our
improvement comes from several aspects: better isoperimetry, smoother
annealing, avoiding transformation to isotropic position and the use of the
"speedy walk" in the analysis.Comment: 23 page
Simulation of quantum walks and fast mixing with classical processes
We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains (LMCs), that is, classical Markov chains with added memory. We show that LMCs can simulate the mixing behavior of any quantum walk, under a commonly satisfied invariance condition. This allows us to answer an open question on how the graph topology ultimately bounds a quantum walk's mixing performance, and that of any stochastic local evolution. The results highlight that speedups in mixing and transport phenomena are not necessarily diagnostic of quantum effects, although superdiffusive spreading is more prominent with quantum walks. The general simulating LMC construction may lead to large memory, yet we show that for the main graphs under study (i.e., lattices) this memory can be brought down to the same size employed in the quantum walks proposed in the literature
- âŠ