Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Expected Complexity for Directional and Multiplicative Voronoi
  Diagrams   While the standard unweighted Voronoi diagram in the plane has linear
worst-case complexity, many of its natural generalizations do not. This paper
considers two such previously studied generalizations, namely multiplicative
and semi Voronoi diagrams. These diagrams both have quadratic worst-case
complexity, though here we show that their expected complexity is linear for
certain natural randomized inputs. Specifically, we argue that the expected
complexity is linear for: (1) semi Voronoi diagrams when the visible direction
is randomly sampled, and (2) for multiplicative diagrams when either weights
are sampled from a constant-sized set, or the more challenging case when
weights are arbitrary but locations are sampled from a square.

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The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom