Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Beyond Triangles: A Distributed Framework for Estimating 3-profiles of
  Large Graphs   We study the problem of approximating the $3$-profile of a large graph.
$3$-profiles are generalizations of triangle counts that specify the number of
times a small graph appears as an induced subgraph of a large graph. Our
algorithm uses the novel concept of $3$-profile sparsifiers: sparse graphs that
can be used to approximate the full $3$-profile counts for a given large graph.
Further, we study the problem of estimating local and ego $3$-profiles, two
graph quantities that characterize the local neighborhood of each vertex of a
graph.
  Our algorithm is distributed and operates as a vertex program over the
GraphLab PowerGraph framework. We introduce the concept of edge pivoting which
allows us to collect $2$-hop information without maintaining an explicit
$2$-hop neighborhood list at each vertex. This enables the computation of all
the local $3$-profiles in parallel with minimal communication.
  We test out implementation in several experiments scaling up to $640$ cores
on Amazon EC2. We find that our algorithm can estimate the $3$-profile of a
graph in approximately the same time as triangle counting. For the harder
problem of ego $3$-profiles, we introduce an algorithm that can estimate
profiles of hundreds of thousands of vertices in parallel, in the timescale of
minutes.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
16
The categories of this paper are: stat