| dc.description.abstract | The primary purpose of this dissertation is in the search for new methods
in which to search for Incomplete Self Orthogonal Latin Squares. As such
a full understanding of the structures involved must be examined, starting
from basic Latin Squares. The structures will be explained and built upon in
order to cover Mutually Orthogonal Latin Squares, Frame Latin Squares and
Self Orthogonal Latin Squares. In addition the related structure Orthogonal
Arrays, will be explained as they relate to Incomplete Self Orthogonal Latin
Squares.
This paper also dedicates time to explaining basic search methods and
optimizations that can be done. The two search methods of focus are the
backtracking algorithm and heuristic searches. In our 6nal method the two
will work together to achieve an improved result. The methods currently
being used to search in parallel are also provided, along with the necessary
backup to there structure.
The main research of this paper is focused on the search for Incomplete
Self Orthogonal Squares. This is done by breaking down the problem into
four separate areas of the square. By separating the blocks it enables us to
work on a smaller problem while eliminating many incorrect solutions. The
solution methodology is broken up into three steps and systematically solving
the individual areas of the square.
By taking advantage of the properties of squares to constrain our search as
much as possible we succeeded in reducing the total search time significantly.
Unfortunately, even with our improvement in the overall search time, no open
incomplete self orthogonal latin square problems could be solved. Full results
and comparisons to existing methods are provided. | |
