The geometrical model is a powerful tool for program
analysis and optimization and forms the basis on which
we build the two parts of this dissertation,
a methodology for incremental loop transformations
and an efficient enumeration technique for parametric
integer sets.

Power consumption for typical embedded multi-media applications
is dominated by the storage of and the access to the large
multi-dimensional arrays they manipulate.
It is now well known that a design methodology for
reducing power consumption and improving system performance should
apply global loop transformations for increasing locality 
and regularity of data accesses.
In the first part of this dissertation,
we propose a two-step global loop transformation approach
consisting of a linear transformation focusing mainly
on regularity, and a translation focusing on locality.
We further develop a refined regularity criterion and show
how to perform the translation step incrementally,
allowing multiple complicated cost functions to be evaluated.

Many compiler optimization techniques depend on the enumeration
of parametric integer sets defined by linear equations.
In the second part of this dissertation,
we present the first implementation of Barvinok's algorithm
applied to the enumeration of parametric polytopes,
extending an earlier implementation of this 
algorithm for a subclass of the enumeration problems we consider,
and providing a significant improvement over 
another implementation based on a different technique.
The resulting enumerator may be obtained as an explicit
function or as a generating function.
We further show that these two representations are polynomially
interconvertible and we discuss some approaches for handling
generalized enumeration problems.