Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sherali-Adams gaps, flow-cover inequalities and generalized
  configurations for capacity-constrained Facility Location   Metric facility location is a well-studied problem for which linear
programming methods have been used with great success in deriving approximation
algorithms. The capacity-constrained generalizations, such as capacitated
facility location (CFL) and lower-bounded facility location (LBFL), have proved
notorious as far as LP-based approximation is concerned: while there are
local-search-based constant-factor approximations, there is no known linear
relaxation with constant integrality gap. According to Williamson and Shmoys
devising a relaxation-based approximation for \cfl\ is among the top 10 open
problems in approximation algorithms.
  This paper advances significantly the state-of-the-art on the effectiveness
of linear programming for capacity-constrained facility location through a host
of impossibility results for both CFL and LBFL. We show that the relaxations
obtained from the natural LP at $\Omega(n)$ levels of the Sherali-Adams
hierarchy have an unbounded gap, partially answering an open question of
\cite{LiS13, AnBS13}. Here, $n$ denotes the number of facilities in the
instance. Building on the ideas for this result, we prove that the standard CFL
relaxation enriched with the generalized flow-cover valid inequalities
\cite{AardalPW95} has also an unbounded gap. This disproves a long-standing
conjecture of \cite{LeviSS12}. We finally introduce the family of proper
relaxations which generalizes to its logical extreme the classic star
relaxation and captures general configuration-style LPs. We characterize the
behavior of proper relaxations for CFL and LBFL through a sharp threshold
phenomenon.

22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph