Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar Disjoint-Paths Completion   introduce {\sc Planar Disjoint Paths Completion}, a completion counterpart of
the Disjoint Paths problem, and study its parameterized complexity. The problem
can be stated as follows: given a, not necessarily connected, plane graph $G,$
$k$ pairs of terminals, and a face $F$ of $G,$ find a minimum-size set of
edges, if one exists, to be added inside $F$ so that the embedding remains
planar and the pairs become connected by $k$ disjoint paths in the augmented
network. Our results are twofold: first, we give an upper bound on the number
of necessary additional edges when a solution exists. This bound is a function
of $k$, independent of the size of $G.$ Second, we show that the problem is
fixed-parameter tractable, in particular, it can be solved in time $f(k)\cdot
n^{2}.$

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The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org