2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 51-56
| author: | Vladimir Deineko, Peter Jonsson, Mikael Klasson and Andrei Krokhin |
|---|---|
| title: | Supermodularity on chains and complexity of maximum constraint satisfaction |
| keywords: |
maximum constraint satisfaction, complexity,
supermodularity, Monge properties, digraph
H
-colouring
|
| abstract: |
In the maximum constraint satisfaction problem (Max CSP),
one is given a finite collection of (possibly weighted)
constraints on overlapping sets of variables, and the goal
is to assign values from a given finite domain to the
variables so as to maximise the number (or the total
weight) of satisfied constraints. This problem is NP-hard
in general so it is natural to study how restricting the
allowed types of constraints affects the complexity of the
problem. In this paper, we show that any Max CSP problem
with a finite set of allowed constraint types, which
includes all constants (i.e. constraints of the form
x=a
), is either solvable in polynomial time or is
NP-complete. Moreover, we present a simple description of
all polynomial-time solvable cases of our problem. This
description uses the well-known combinatorial property of
supermodularity.
|
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| reference: | Vladimir Deineko and Peter Jonsson and Mikael Klasson and Andrei Krokhin (2005), Supermodularity on chains and complexity of maximum constraint satisfaction, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 51-56 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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