Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximability of Integer Programming with Generalised Constraints   We study a family of problems, called \prob{Maximum Solution}, where the
objective is to maximise a linear goal function over the feasible integer
assignments to a set of variables subject to a set of constraints. When the
domain is Boolean (i.e. restricted to $\{0,1\}$), the maximum solution problem
is identical to the well-studied \prob{Max Ones} problem, and the
approximability is completely understood for all restrictions on the underlying
constraints [Khanna et al., SIAM J. Comput., 30 (2001), pp. 1863-1920]. We
continue this line of research by considering domains containing more than two
elements. We present two main results: a complete classification for the
approximability of all maximal constraint languages over domains of cardinality
at most 4, and a complete classification of the approximability of the problem
when the set of allowed constraints contains all permutation constraints. Under
the assumption that a conjecture due to Szczepara holds, we give a complete
classification for all maximal constraint languages. These classes of languages
are well-studied in universal algebra and computer science; they have, for
instance, been considered in connection with machine learning and constraint
satisfaction. Our results are proved by using algebraic results from clone
theory and the results indicates that this approach is very powerful for
classifying the approximability of certain optimisation problems.

25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph