Brett Stevens
(Department of Mathematics and Statistics, Simon Fraser University University)
Resolutions and Resolvability: Substructures in combinatorial designs and
their utility towards solving hard combinatorial optimization problems
Abstract
I will give a talk, accessible to a broad audience, describing 3 central
research areas and a framework unifying them. A resolution class
in a design is a set of disjoint blocks whose union
is the entire set. A design is resolvable if it can be partitioned
into resolutions. I will discuss the use of resolutions and resolvability
to optimize the construction of covering and packing arrays, both hard
combinatorial optimization problems with important industrial applications.
I will close with the use of resolvable designs to solve scheduling problems.
In all cases I will give background information, definitions and applications,
state current results and discuss future directions. |
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