The existence of a PSAKS for the Rural Postman Problem parameterized by c

Let $(G,R,\omega)$ be an instance of the Rural Postman Problem (RPP), and let $c$ denote the number of connected components of the required-edge subgraph. A polynomial-size approximate kernelization scheme (PSAKS) for RPP with respect to the parameter $c$ is a parameterized approximation scheme that reduces instances to equivalent instances whose size is bounded polynomially in $c$ and the approximation parameter.

RPP PSAKS conjecture. RPP has a PSAKS with respect to the parameter $c$.

The conjecture concerns whether approximate data reduction can yield polynomial-size kernels when the number of connected components of the required-edge subgraph is the parameter. The surrounding results establish approximation and kernelization in several restricted weight regimes, but do not resolve the general existence of such a PSAKS.