Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimum Enclosing Circle of a Set of Static Points with Dynamic Weight
  from One Free Point   Given a set $S$ of $n$ static points and a free point $p$ in the Euclidean
plane, we study a new variation of the minimum enclosing circle problem, in
which a dynamic weight that equals to the reciprocal of the distance from the
free point $p$ to the undetermined circle center is included. In this work, we
prove the optimal solution of the new problem is unique and lies on the
boundary of the farthest-point Voronoi diagram of $S$, once $p$ does not
coincide with any vertex of the convex hull of $S$. We propose a tree structure
constructed from the boundary of the farthest-point Voronoi diagram and use the
hierarchical relationship between edges to locate the optimal solution. The
plane could be divide into at most $3n-4$ non-overlapping regions. When $p$
lies in one of the regions, the optimal solution locates at one node or lies on
the interior of one edge in the boundary of the farthest-point Voronoi diagram.
Moreover, we apply the new variation to calculate the maximum displacement of
one point $p$ under the condition that the displacements of points in $S$ are
restricted in 2D rigid motion.

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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: ao-sci