  The paper considers the SUPPORTED model of distributed computing introduced
by Schmid and Suomela [HotSDN'13], generalizing the LOCAL and CONGEST models.
In this framework, multiple instances of the same problem, differing from each
other by the subnetwork to which they apply, recur over time, and need to be
solved efficiently online. To do that, one may rely on an initial preprocessing
phase for computing some useful information. This preprocessing phase makes it
possible, in some cases, to overcome locality-based time lower bounds.
  A first contribution of the current paper is expanding the spectrum of
problem types to which the SUPPORTED model applies. In addition to
subnetwork-defined recurrent problems, we introduce also recurrent problems of
two additional types: (i) instances defined by partial client sets, and (ii)
instances defined by partially fixed outputs.
  Our second contribution is illustrating the versatility of the SUPPORTED
framework by examining recurrent variants of three classical graph problems.
The first problem is Minimum Client Dominating Set (CDS), a recurrent version
of the classical dominating set problem with each recurrent instance requiring
us to dominate a partial client set. We provide a constant time approximation
scheme for CDS on trees and planar graphs.
  The second problem is Color Completion (CC), a recurrent version of the
coloring problem in which each recurrent instance comes with a partially fixed
coloring (of some of the vertices) that must be completed. We study the minimum
number of new colors and the minimum total number of colors necessary for
completing this task.
  The third problem we study is a recurrent version of Locally Checkable
Labellings (LCL) on paths of length $n$. We show that such problems have
complexities that are either $\Theta(1)$ or $\Theta(n)$, extending the results
of Foerster et al. [INFOCOM'19].
