Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deterministic Fully Dynamic Data Structures for Vertex Cover and
  Matching   We present the first deterministic data structures for maintaining
approximate minimum vertex cover and maximum matching in a fully dynamic graph
$G = (V,E)$, with $|V| = n$ and $|E| =m$, in $o(\sqrt{m}\,)$ time per update.
In particular, for minimum vertex cover we provide deterministic data
structures for maintaining a $(2+\eps)$ approximation in $O(\log n/\eps^2)$
amortized time per update.
  For maximum matching, we show how to maintain a $(3+\eps)$ approximation in
$O(\min(\sqrt{n}/\epsilon, m^{1/3}/\eps^2))$ {\em amortized} time per update,
and a $(4+\eps)$ approximation in $O(m^{1/3}/\eps^2)$ {\em worst-case} time per
update. Our data structure for fully dynamic minimum vertex cover is
essentially near-optimal and settles an open problem by Onak and Rubinfeld from
STOC' 2010.

35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom