Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Min st-Cut Oracle for Planar Graphs with Near-Linear Preprocessing Time   For an undirected $n$-vertex planar graph $G$ with non-negative edge-weights,
we consider the following type of query: given two vertices $s$ and $t$ in $G$,
what is the weight of a min $st$-cut in $G$? We show how to answer such queries
in constant time with $O(n\log^4n)$ preprocessing time and $O(n\log n)$ space.
We use a Gomory-Hu tree to represent all the pairwise min cuts implicitly.
Previously, no subquadratic time algorithm was known for this problem. Since
all-pairs min cut and the minimum cycle basis are dual problems in planar
graphs, we also obtain an implicit representation of a minimum cycle basis in
$O(n\log^4n)$ time and $O(n\log n)$ space. Additionally, an explicit
representation can be obtained in $O(C)$ time and space where $C$ is the size
of the basis.
  These results require that shortest paths are unique. This can be guaranteed
either by using randomization without overhead, or deterministically with an
additional $\log^2 n$ factor in the preprocessing times.

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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: math
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph