Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved approximation algorithm for Fault-Tolerant Facility Placement   We consider the Fault-Tolerant Facility Placement problem ($FTFP$), which is
a generalization of the classical Uncapacitated Facility Location problem
($UFL$). In the $FTFP$ problem we have a set of clients $C$ and a set of
facilities $F$. Each facility $i \in F$ can be opened many times. For each
opening of facility $i$ we pay $f_i \geq 0$. Our goal is to connect each client
$j \in C$ with $r_j \geq 1$ open facilities in a way that minimizes the total
cost of open facilities and established connections.
  In a series of recent papers $FTFP$ was essentially reduced to $FTFL$ and
then to $UFL$ showing it could be approximated with ratio $1.575$. In this
paper we show that $FTFP$ can actually be approximated even better. We consider
approximation ratio as a function of $r = min_{j \in C} r_j$ (minimum
requirement of a client). With increasing $r$ the approximation ratio of our
algorithm $\lambda_r$ converges to one. Furthermore, for $r > 1$ the value of
$\lambda_r$ is less than 1.463 (hardness of approximation of $UFL$). We also
show a lower bound of 1.278 for the approximability of the Fault-Tolerant
Facility Location problem ($FTFL$) for arbitrary $r$. Already for $r > 3$ we
obtain that $FTFP$ can be approximated with ratio 1.275, showing that under
standard complexity theoretic assumptions $FTFP$ is strictly better
approximable than $FTFL$.

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The categories of this paper are: math
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom