Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Matching Problem in General Graphs is in Quasi-NC   We show that the perfect matching problem in general graphs is in Quasi-NC.
That is, we give a deterministic parallel algorithm which runs in $O(\log^3 n)$
time on $n^{O(\log^2 n)}$ processors. The result is obtained by a
derandomization of the Isolation Lemma for perfect matchings, which was
introduced in the classic paper by Mulmuley, Vazirani and Vazirani [1987] to
obtain a Randomized NC algorithm.
  Our proof extends the framework of Fenner, Gurjar and Thierauf [2016], who
proved the analogous result in the special case of bipartite graphs. Compared
to that setting, several new ingredients are needed due to the significantly
more complex structure of perfect matchings in general graphs. In particular,
our proof heavily relies on the laminar structure of the faces of the perfect
matching polytope.

32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph