Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Beating Greedy For Approximating Reserve Prices in Multi-Unit VCG
  Auctions   We study the problem of finding personalized reserve prices for unit-demand
buyers in multi-unit eager VCG auctions with correlated buyers. The input to
this problem is a dataset of submitted bids of $n$ buyers in a set of auctions.
The goal is to find a vector of reserve prices, one for each buyer, that
maximizes the total revenue across all auctions.
  Roughgarden and Wang (2016) showed that this problem is APX-hard but admits a
greedy $\frac{1}{2}$-approximation algorithm. Later, Derakhshan, Golrezai, and
Paes Leme (2019) gave an LP-based algorithm achieving a $0.68$-approximation
for the (important) special case of the problem with a single-item, thereby
beating greedy. We show in this paper that the algorithm of Derakhshan et al.
in fact does not beat greedy for the general multi-item problem. This raises
the question of whether or not the general problem admits a
better-than-$\frac{1}{2}$ approximation.
  In this paper, we answer this question in the affirmative and provide a
polynomial-time algorithm with a significantly better approximation-factor of
$0.63$. Our solution is based on a novel linear programming formulation, for
which we propose two different rounding schemes. We prove that the best of
these two and the no-reserve case (all-zero vector) is a $0.63$-approximation.

15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol