Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to Walk Your Dog in the Mountains with No Magic Leash   We describe a $O(\log n )$-approximation algorithm for computing the
homotopic \Frechet distance between two polygonal curves that lie on the
boundary of a triangulated topological disk. Prior to this work, algorithms
were known only for curves on the Euclidean plane with polygonal obstacles.
  A key technical ingredient in our analysis is a $O(\log n)$-approximation
algorithm for computing the minimum height of a homotopy between two curves. No
algorithms were previously known for approximating this parameter.
Surprisingly, it is not even known if computing either the homotopic \Frechet
distance, or the minimum height of a homotopy, is in NP.

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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th