Research@StAndrews
 
The University of St Andrews

Research@StAndrews:FullText >
Computer Science (School of) >
Computer Science >
Computer Science Theses >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/1718
This item has been viewed 17 times in the last year. View Statistics

Files in This Item:

File Description SizeFormat
Andrew GraylandPhDThesis.pdf1.55 MBAdobe PDFView/Open
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.
URI: http://hdl.handle.net/10023/1718
Type: Thesis
Publisher: University of St Andrews
Appears in Collections:Computer Science Theses



This item is protected by original copyright

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

 

DSpace Software Copyright © 2002-2012  Duraspace - Feedback
For help contact: Digital-Repository@st-andrews.ac.uk | Copyright for this page belongs to St Andrews University Library | Terms and Conditions (Cookies)