Section:
New Results
Automata and Matrix Models
Participants :
Nicolas Beldiceanu, Mats Carlsson, Pierre Flener, Justin Pearson.
Matrix models are ubiquitous for constraint problems. Many such
problems have a matrix of variables , with the same
constraint defined by a finite-state automaton on
each row of and a global cardinality constraint
on each column of . We give two
methods for deriving, by double counting, necessary conditions on the
cardinality variables of the constraints from the automaton
. The first method yields linear necessary conditions
and simple arithmetic constraints. The second method introduces the
cardinality automaton, which abstracts the overall behaviour
of all the row automata and can be encoded by a set of linear
constraints. We also provide a arc-consistency filtering algorithm
for the conjunction of lexicographic ordering constraints between
adjacent rows of and (possibly different) automaton
constraints on the rows. We evaluate the impact of our methods in
terms of runtime and search effort on a large set of nurse rostering
problem instances.
The corresponding paper
On Matrices, Automata, and Double Counting in Constraint Programming [11]
was published in the
Constraints journal.
Previous | 
Home