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|Title: ||Automated static symmetry breaking in constraint satisfaction problems|
|Authors: ||Grayland, Andrews|
|Supervisors: ||Miguel, Ian|
|Issue Date: ||2011|
|Abstract: ||Variable symmetries in constraint satisfaction problems can be broken by
adding lexicographic ordering constraints. Existing general methods of generating
such sets of ordering constraints can produce a huge number of additional
constraints. This adds an unacceptable overhead to the solving process. Methods
exist by which this large set of constraints can be reduced to a much smaller
set automatically, but their application is also prohibitively costly. In contrast,
this thesis takes a bottom up approach to generating symmetry breaking constraints.
This will involve examining some commonly-occurring families of
mathematical groups and deriving a general formula to produce a minimal set
of ordering constraints which are sufficient to break all of the symmetry that
each group describes.
In some cases it is known that there exists no manageable sized sets of
constraints to break all symmetries. One example of this occurs with matrix
row and column symmetries. In such cases, incomplete symmetry breaking has
been used to great effect. Double lex is a commonly used incomplete symmetry
breaking technique for row and column symmetries. This thesis also describes
another similar method which compares favourably to double lex.
The general formulae investigated are used as building blocks to generate
small sets of ordering constraints for more complex groups, constructed by
combining smaller groups.
Through the utilisation of graph automorphism tools and the groups and
permutations software GAP we provide a method of defining variable symmetries
in a problem as a group. Where this group can be described as the product
of smaller groups, with known general formulae, we can construct a minimal
set of ordering constraints for that problem automatically. In summary, this thesis provides the theoretical background necessary to
apply efficient static symmetry breaking to constraint satisfaction problems. It
also goes further, describing how this process can be automated to remove the
necessity of having an expert CP practitioner, thus opening the field to a larger
number of potential users.|
|Publisher: ||University of St Andrews|
|Appears in Collections:||Computer Science Theses|
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