Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perpetual maintenance of machines with different urgency requirements   A garden $G$ is populated by $n\ge 1$ bamboos $b_1, b_2, ..., b_n$ with the
respective daily growth rates $h_1 \ge h_2 \ge \dots \ge h_n$. It is assumed
that the initial heights of bamboos are zero. The robotic gardener maintaining
the garden regularly attends bamboos and trims them to height zero according to
some schedule. The Bamboo Garden Trimming Problem (BGT) is to design a
perpetual schedule of cuts to maintain the elevation of the bamboo garden as
low as possible. The bamboo garden is a metaphor for a collection of machines
which have to be serviced, with different frequencies, by a robot which can
service only one machine at a time. The objective is to design a perpetual
schedule of servicing which minimizes the maximum (weighted) waiting time for
servicing.
  We consider two variants of BGT. In discrete BGT the robot trims only one
bamboo at the end of each day. In continuous BGT the bamboos can be cut at any
time, however, the robot needs time to move from one bamboo to the next.
  For discrete BGT, we show a simple $4$-approximation algorithm and, by
exploiting relationship between BGT and the classical Pinwheel scheduling
problem, we derive a $2$-approximation algorithm for the general case and a
tighter approximation when the growth rates are balanced. A by-product of this
last approximation algorithm is that it settles one of the conjectures about
the Pinwheel problem. For continuous BGT, we propose approximation algorithms
which achieve approximation ratios $O(\log (h_1/h_n))$ and $O(\log n)$.

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The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
3
The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int