Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simpler and Stronger Approaches for Non-Uniform Hypergraph Matching and
  the F\"uredi, Kahn, and Seymour Conjecture   A well-known conjecture of F\"uredi, Kahn, and Seymour (1993) on non-uniform
hypergraph matching states that for any hypergraph with edge weights $w$, there
exists a matching $M$ such that the inequality $\sum_{e\in M} g(e) w(e) \geq
\mathrm{OPT}_{\mathrm{LP}}$ holds with $g(e)=|e|-1+\frac{1}{|e|}$, where
$\mathrm{OPT}_{\mathrm{LP}}$ denotes the optimal value of the canonical LP
relaxation.
  While the conjecture remains open, the strongest result towards it was very
recently obtained by Brubach, Sankararaman, Srinivasan, and Xu
(2020)---building on and strengthening prior work by Bansal, Gupta, Li, Mestre,
Nagarajan, and Rudra (2012)---showing that the aforementioned inequality holds
with $g(e)=|e|+O(|e|\exp(-|e|))$.
  Actually, their method works in a more general sampling setting, where, given
a point $x$ of the canonical LP relaxation, the task is to efficiently sample a
matching $M$ containing each edge $e$ with probability at least
$\frac{x(e)}{g(e)}$.
  We present simpler and easy-to-analyze procedures leading to improved
results. More precisely, for any solution $x$ to the canonical LP, we introduce
a simple algorithm based on exponential clocks for Brubach et al.'s sampling
setting achieving $g(e)=|e|-(|e|-1)x(e)$.
  Apart from the slight improvement in $g$, our technique may open up new ways
to attack the original conjecture.
  Moreover, we provide a short and arguably elegant analysis showing that a
natural greedy approach for the original setting of the conjecture shows the
inequality for the same $g(e)=|e|-(|e|-1)x(e)$ even for the more general
hypergraph $b$-matching problem.

31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int