  We define a new notion of compressibility of a set of numbers through the
dynamics of a polynomial function. We provide approaches to solve the problem
by reducing it to the multi-criteria traveling salesman problem through a
series of transformations. We then establish computational complexity results
by giving some NP-completeness proofs. We also discuss about a notion of
$\epsilon$ K-compressibility of a set, with regard to lossy compression and
deduce the necessary condition for the given set to be $\epsilon$
K-compressible. Finally, we conclude by providing a list of open problems
solutions to which could extend the applicability the our technique.
