Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kinetic Data Structures for the Semi-Yao Graph and All Nearest Neighbors
  in R^d   This paper presents a simple kinetic data structure for maintaining all the
nearest neighbors of a set of $n$ moving points in $\mathbb{R}^d$, where the
trajectory of each point is an algebraic function of at most constant degree
$s$. The approach is based on maintaining the edges of the Semi-Yao graph, a
sparse graph whose edge set includes the pairs of nearest neighbors as a
subset.
  Our kinetic data structure (KDS) for maintaining all the nearest neighbors is
deterministic. It processes $O(n^2\beta_{2s+2}^2(n)\log n)$ events with a total
cost of $O(n^2\beta_{2s+2}(n)\log^{d+1} n)$. Here, $\beta_s(n)$ is an extremely
slow-growing function. The best previous KDS for all the nearest neighbors in $
\mathbb{R}^d$ is by Agarwal, Kaplan, and Sharir (TALG 2008). It is a randomized
result. Our structure and analysis are simpler than theirs. Also, we improve
their result by a factor of $\log^d n$ in the number of events and by a $\log
n$ factor in the total cost.
  This paper generalizes and improves the 2013 work of Rahmati, King and
Whitesides (SoCG 2013) on maintaining the Semi-Yao graph in $\mathbb{R}^2$; its
new technique provides the first KDS for the Semi-Yao graph in $\mathbb{R}^d$.
Our KDS is local in the worst case, meaning that only a constant number of
events is associated with any one point at any time.
  For maintaining all the nearest neighbors, neither our KDS nor the KDS by
Agarwal~\etal~is local, and furthermore, each event in our KDS and in their KDS
is handled in polylogarithmic time in an amortized sense.
  Finally, in this paper, we also give a KDS for maintenance of all the
$(1+\epsilon)$-nearest neighbors which is local and each event can be handled
in a polylogarithmic worst-case time.

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The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ