Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive Computation of the Discrete Fr\'echet Distance   The discrete Fr{\'e}chet distance is a measure of similarity between point
sequences which permits to abstract differences of resolution between the two
curves, approximating the original Fr{\'e}chet distance between curves. Such
distance between sequences of respective length $n$ and $m$ can be computed in
time within $O(nm)$ and space within $O(n+m)$ using classical dynamic
programing techniques, a complexity likely to be optimal in the worst case over
sequences of similar lenght unless the Strong Exponential Hypothesis is proved
incorrect. We propose a parameterized analysis of the computational complexity
of the discrete Fr{\'e}chet distance in fonction of the area of the dynamic
program matrix relevant to the computation, measured by its \emph{certificate
width} $\omega$. We prove that the discrete Fr{\'e}chet distance can be
computed in time within $((n+m)\omega)$ and space within $O(n+m+\omega)$.

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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
30
The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org