Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Good Illumination of Minimum Range   A point p is 1-well illuminated by a set F of n point lights if p lies in the
interior of the convex hull of F. This concept corresponds to triangle-guarding
or well-covering. In this paper we consider the illumination range of the light
sources as a parameter to be optimized. First, we solve the problem of
minimizing the light sources' illumination range to 1-well illuminate a given
point p. We also compute a minimal set of light sources that 1-well illuminates
p with minimum illumination range. Second, we solve the problem of minimizing
the light sources' illumination range to 1-well illuminate all the points of a
line segment with an O(n^2) algorithm. Finally, we give an O(n^2 log n)
algorithm for preprocessing the data so that one can obtain the illumination
range needed to 1-well illuminate a point of a line segment in O(log n) time.
These results can be applied to solve problems of 1-well illuminating a
trajectory by approaching it to a polygonal path.

27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
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The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
18
The categories of this paper are: econ
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The categories of this paper are: ao-sci