Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved Approximation Algorithms for Matroid and Knapsack Median
  Problems and Applications   We consider the {\em matroid median} problem \cite{KrishnaswamyKNSS11},
wherein we are given a set of facilities with opening costs and a matroid on
the facility-set, and clients with demands and connection costs, and we seek to
open an independent set of facilities and assign clients to open facilities so
as to minimize the sum of the facility-opening and client-connection costs. We
give a simple 8-approximation algorithm for this problem based on LP-rounding,
which improves upon the 16-approximation in \cite{KrishnaswamyKNSS11}. Our
techniques illustrate that much of the work involved in the rounding algorithm
of in \cite{KrishnaswamyKNSS11} can be avoided by first converting the LP
solution to a half-integral solution, which can then be rounded to an integer
solution using a simple uncapacitated-facility-location (UFL) style clustering
step. We illustrate the power of these ideas by deriving: (a) a
24-approximation algorithm for matroid median with penalties, which is a vast
improvement over the 360-approximation obtained in \cite{KrishnaswamyKNSS11};
and (b) an 8-approximation for the {\em two-matroid median} problem, a
generalization of matroid median that we introduce involving two matroids. We
show that a variety of seemingly disparate facility-location problems
considered in the literature---data placement problem, mobile facility
location, $k$-median forest, metric uniform minimum-latency UFL---in fact
reduce to the matroid median or two-matroid median problems, and thus obtain
improved approximation guarantees for all these problems. Our techniques also
yield an improvement for the knapsack median problem.

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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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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: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph