Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Soft constraint abstraction based on semiring homomorphism   The semiring-based constraint satisfaction problems (semiring CSPs), proposed
by Bistarelli, Montanari and Rossi \cite{BMR97}, is a very general framework of
soft constraints. In this paper we propose an abstraction scheme for soft
constraints that uses semiring homomorphism. To find optimal solutions of the
concrete problem, the idea is, first working in the abstract problem and
finding its optimal solutions, then using them to solve the concrete problem.
  In particular, we show that a mapping preserves optimal solutions if and only
if it is an order-reflecting semiring homomorphism. Moreover, for a semiring
homomorphism $\alpha$ and a problem $P$ over $S$, if $t$ is optimal in
$\alpha(P)$, then there is an optimal solution $\bar{t}$ of $P$ such that
$\bar{t}$ has the same value as $t$ in $\alpha(P)$.

26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom