56 research outputs found
Distributed Triangle Counting in the Graphulo Matrix Math Library
Triangle counting is a key algorithm for large graph analysis. The Graphulo
library provides a framework for implementing graph algorithms on the Apache
Accumulo distributed database. In this work we adapt two algorithms for
counting triangles, one that uses the adjacency matrix and another that also
uses the incidence matrix, to the Graphulo library for server-side processing
inside Accumulo. Cloud-based experiments show a similar performance profile for
these different approaches on the family of power law Graph500 graphs, for
which data skew increasingly bottlenecks. These results motivate the design of
skew-aware hybrid algorithms that we propose for future work.Comment: Honorable mention in the 2017 IEEE HPEC's Graph Challeng
Catching the head, tail, and everything in between: a streaming algorithm for the degree distribution
The degree distribution is one of the most fundamental graph properties of
interest for real-world graphs. It has been widely observed in numerous domains
that graphs typically have a tailed or scale-free degree distribution. While
the average degree is usually quite small, the variance is quite high and there
are vertices with degrees at all scales. We focus on the problem of
approximating the degree distribution of a large streaming graph, with small
storage. We design an algorithm headtail, whose main novelty is a new estimator
of infrequent degrees using truncated geometric random variables. We give a
mathematical analysis of headtail and show that it has excellent behavior in
practice. We can process streams will millions of edges with storage less than
1% and get extremely accurate approximations for all scales in the degree
distribution.
We also introduce a new notion of Relative Hausdorff distance between tailed
histograms. Existing notions of distances between distributions are not
suitable, since they ignore infrequent degrees in the tail. The Relative
Hausdorff distance measures deviations at all scales, and is a more suitable
distance for comparing degree distributions. By tracking this new measure, we
are able to give strong empirical evidence of the convergence of headtail
Graph Sample and Hold: A Framework for Big-Graph Analytics
Sampling is a standard approach in big-graph analytics; the goal is to
efficiently estimate the graph properties by consulting a sample of the whole
population. A perfect sample is assumed to mirror every property of the whole
population. Unfortunately, such a perfect sample is hard to collect in complex
populations such as graphs (e.g. web graphs, social networks etc), where an
underlying network connects the units of the population. Therefore, a good
sample will be representative in the sense that graph properties of interest
can be estimated with a known degree of accuracy. While previous work focused
particularly on sampling schemes used to estimate certain graph properties
(e.g. triangle count), much less is known for the case when we need to estimate
various graph properties with the same sampling scheme. In this paper, we
propose a generic stream sampling framework for big-graph analytics, called
Graph Sample and Hold (gSH). To begin, the proposed framework samples from
massive graphs sequentially in a single pass, one edge at a time, while
maintaining a small state. We then show how to produce unbiased estimators for
various graph properties from the sample. Given that the graph analysis
algorithms will run on a sample instead of the whole population, the runtime
complexity of these algorithm is kept under control. Moreover, given that the
estimators of graph properties are unbiased, the approximation error is kept
under control. Finally, we show the performance of the proposed framework (gSH)
on various types of graphs, such as social graphs, among others
FLEET: Butterfly Estimation from a Bipartite Graph Stream
We consider space-efficient single-pass estimation of the number of
butterflies, a fundamental bipartite graph motif, from a massive bipartite
graph stream where each edge represents a connection between entities in two
different partitions. We present a space lower bound for any streaming
algorithm that can estimate the number of butterflies accurately, as well as
FLEET, a suite of algorithms for accurately estimating the number of
butterflies in the graph stream. Estimates returned by the algorithms come with
provable guarantees on the approximation error, and experiments show good
tradeoffs between the space used and the accuracy of approximation. We also
present space-efficient algorithms for estimating the number of butterflies
within a sliding window of the most recent elements in the stream. While there
is a significant body of work on counting subgraphs such as triangles in a
unipartite graph stream, our work seems to be one of the few to tackle the case
of bipartite graph streams.Comment: This is the author's version of the work. It is posted here by
permission of ACM for your personal use. Not for redistribution. The
definitive version was published in Seyed-Vahid Sanei-Mehri, Yu Zhang, Ahmet
Erdem Sariyuce and Srikanta Tirthapura. "FLEET: Butterfly Estimation from a
Bipartite Graph Stream". The 28th ACM International Conference on Information
and Knowledge Managemen
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