Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small Space Stream Summary for Matroid Center   In the matroid center problem, which generalizes the $k$-center problem, we
need to pick a set of centers that is an independent set of a matroid with rank
$r$. We study this problem in streaming, where elements of the ground set
arrive in the stream. We first show that any randomized one-pass streaming
algorithm that computes a better than $\Delta$-approximation for
partition-matroid center must use $\Omega(r^2)$ bits of space, where $\Delta$
is the aspect ratio of the metric and can be arbitrarily large. This shows a
quadratic separation between matroid center and $k$-center, for which the
Doubling algorithm gives an $8$-approximation using $O(k)$-space and one pass.
To complement this, we give a one-pass algorithm for matroid center that stores
at most $O(r^2\log(1/\varepsilon)/\varepsilon)$ points (viz., stream summary)
among which a $(7+\varepsilon)$-approximate solution exists, which can be found
by brute force, or a $(17+\varepsilon)$-approximation can be found with an
efficient algorithm. If we are allowed a second pass, we can compute a
$(3+\varepsilon)$-approximation efficiently; this also achieves almost the
known-best approximation ratio (of $3+\varepsilon$) with total running time of
$O((nr + r^{3.5})\log(1/\varepsilon)/\varepsilon + r^2(\log
\Delta)/\varepsilon)$, where $n$ is the number of input points.
  We also consider the problem of matroid center with $z$ outliers and give a
one-pass algorithm that outputs a set of
$O((r^2+rz)\log(1/\varepsilon)/\varepsilon)$ points that contains a
$(15+\varepsilon)$-approximate solution. Our techniques extend to knapsack
center and knapsack center with outliers in a straightforward way, and we get
algorithms that use space linear in the size of a largest feasible set (as
opposed to quadratic space for matroid center).

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The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
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The categories of this paper are: q-alg
2
The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph