Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faster motif counting via succinct color coding and adaptive sampling   We address the problem of computing the distribution of induced connected
subgraphs, aka \emph{graphlets} or \emph{motifs}, in large graphs. The current
state-of-the-art algorithms estimate the motif counts via uniform sampling, by
leveraging the color coding technique by Alon, Yuster and Zwick. In this work
we extend the applicability of this approach, by introducing a set of
algorithmic optimizations and techniques that reduce the running time and space
usage of color coding and improve the accuracy of the counts. To this end, we
first show how to optimize color coding to efficiently build a compact table of
a representative subsample of all graphlets in the input graph. For $8$-node
motifs, we can build such a table in one hour for a graph with $65$M nodes and
$1.8$B edges, which is $2000$ times larger than the state of the art. We then
introduce a novel adaptive sampling scheme that breaks the "additive error
barrier" of uniform sampling, guaranteeing multiplicative approximations
instead of just additive ones. This allows us to count not only the most
frequent motifs, but also extremely rare ones. For instance, on one graph we
accurately count nearly $10.000$ distinct $8$-node motifs whose relative
frequency is so small that uniform sampling would literally take centuries to
find them. Our results show that color coding is still the most promising
approach to scalable motif counting.

2
The categories of this paper are: math
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas