Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sublinear-Time Algorithms for Counting Star Subgraphs with Applications
  to Join Selectivity Estimation   We study the problem of estimating the value of sums of the form $S_p
\triangleq \sum \binom{x_i}{p}$ when one has the ability to sample $x_i \geq 0$
with probability proportional to its magnitude. When $p=2$, this problem is
equivalent to estimating the selectivity of a self-join query in database
systems when one can sample rows randomly. We also study the special case when
$\{x_i\}$ is the degree sequence of a graph, which corresponds to counting the
number of $p$-stars in a graph when one has the ability to sample edges
randomly.
  Our algorithm for a $(1 \pm \varepsilon)$-multiplicative approximation of
$S_p$ has query and time complexities $\O(\frac{m \log \log n}{\epsilon^2
S_p^{1/p}})$. Here, $m=\sum x_i/2$ is the number of edges in the graph, or
equivalently, half the number of records in the database table. Similarly, $n$
is the number of vertices in the graph and the number of unique values in the
database table. We also provide tight lower bounds (up to polylogarithmic
factors) in almost all cases, even when $\{x_i\}$ is a degree sequence and one
is allowed to use the structure of the graph to try to get a better estimate.
We are not aware of any prior lower bounds on the problem of join selectivity
estimation.
  For the graph problem, prior work which assumed the ability to sample only
\emph{vertices} uniformly gave algorithms with matching lower bounds [Gonen,
Ron, and Shavitt. \textit{SIAM J. Comput.}, 25 (2011), pp. 1365-1411]. With the
ability to sample edges randomly, we show that one can achieve faster
algorithms for approximating the number of star subgraphs, bypassing the lower
bounds in this prior work. For example, in the regime where $S_p\leq n$, and
$p=2$, our upper bound is $\tilde{O}(n/S_p^{1/2})$, in contrast to their
$\Omega(n/S_p^{1/3})$ lower bound when no random edge queries are available.

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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys