Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Randomized Strategyproof Mechanisms for Facility Location and the
  Mini-Sum-of-Squares Objective   We consider the problem of locating a public facility on a line, where a set
of $n$ strategic agents report their \emph{locations} and a mechanism
determines, either deterministically or randomly, the location of the facility.
Game theoretic perspectives of the facility location problem advanced in two
main directions. The first direction is concerned with the characterization of
\emph{strategyproof} (SP) mechanisms; i.e., mechanisms that induce truthful
reporting as a dominant strategy; and the second direction quantifies how well
various objective functions can be approximated when restricted to SP
mechanisms. The current paper provides contributions in both directions. First,
we construct a parameterized randomized SP mechanism, and show that all of the
previously proposed deterministic and randomized SP mechanisms for the current
settings can be formalized as special cases of this mechanism. Second, we give
tight results for the approximation ratio of SP mechanisms with respect to the
objective of minimizing the sum of squares of distances to the agents
(\emph{miniSOS}). Holzman \cite{Holzman1990} provided an axiomatic foundation
for this function, showing that it is the unique function that satisfies
unanimity, continuity and invariance. We devise a randomized mechanism that
gives a 1.5-approximation for the miniSOS function, and show that no other
randomized SP mechanism can provide a better approximation. This mechanism
chooses the average location with probability 1/2 and a \emph{random dictator}
with probability 1/2. For deterministic mechanisms, we show that the median
mechanism provides a 2-approximation, and this is tight. Together, our study
provides fundamental understanding of the miniSOS objective function and makes
a step toward the characterization of randomized SP facility location
mechanisms.

29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
18
The categories of this paper are: econ