Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modem Illumination of Monotone Polygons   We study a generalization of the classical problem of the illumination of
polygons. Instead of modeling a light source we model a wireless device whose
radio signal can penetrate a given number $k$ of walls. We call these objects
$k$-modems and study the minimum number of $k$-modems sufficient and sometimes
necessary to illuminate monotone and monotone orthogonal polygons. We show that
every monotone polygon with $n$ vertices can be illuminated with $\big\lceil
\frac{n-2}{2k+3} \big\rceil$ $k$-modems. In addition, we exhibit examples of
monotone polygons requiring at least $\lceil \frac {n-2} {2k+3}\rceil$
$k$-modems to be illuminated.
  For monotone orthogonal polygons with $n$ vertices we show that for $k=1$ and
for even $k$, every such polygon can be illuminated with $\big\lceil
\frac{n-2}{2k+4} \big\rceil$ $k$-modems, while for odd $k\geq3$, $\big\lceil
\frac{n-2}{2k+6} \big\rceil$ $k$-modems are always sufficient. Further, by
presenting according examples of monotone orthogonal polygons, we show that
both bounds are tight.

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys