Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sweeping costs of planar domains   Let D be a Jordan domain in the plane. We consider a pursuit-evasion,
contamination clearing, or sensor sweep problem in which the pursuer at each
point in time is modeled by a continuous curve, called the sensor curve. Both
time and space are continuous, and the intruders are invisible to the pursuer.
Given D, what is the shortest length of a sensor curve necessary to provide a
sweep of domain D, so that no continuously-moving intruder in D can avoid being
hit by the curve? We define this length to be the sweeping cost of D. We
provide an analytic formula for the sweeping cost of any Jordan domain in terms
of the geodesic Frechet distance between two curves on the boundary of D with
non-equal winding numbers. As a consequence, we show that the sweeping cost of
any convex domain is equal to its width, and that a convex domain of unit area
with maximal sweeping cost is the equilateral triangle.

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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph