  In this paper, we study the computation of shortest paths within the
\emph{geometric amoebot model}, a commonly used model for programmable matter.
Shortest paths are essential for various tasks and therefore have been heavily
investigated in many different contexts. For example, in the programmable
matter context, which is the focus of this paper, Kostitsyna et al. have
utilized shortest path trees to transform one amoebot structure into another
[DISC, 2023]. We consider the \emph{reconfigurable circuit extension} of the
model where this amoebot structure is able to interconnect amoebots by
so-called circuits. These circuits permit the instantaneous transmission of
simple signals between connected amoebots.
  We propose two distributed algorithms for the \emph{shortest path forest
problem} where, given a set of $k$ sources and a set of $\ell$ destinations,
the amoebot structure has to compute a forest that connects each destination to
its closest source on a shortest path. For hole-free structures, the first
algorithm constructs a shortest path tree for a single source within $O(\log
\ell)$ rounds, and the second algorithm a shortest path forest for an arbitrary
number of sources within $O(\log n \log^2 k)$ rounds. The former algorithm also
provides an $O(1)$ rounds solution for the \emph{single pair shortest path
problem} (SPSP) and an $O(\log n)$ rounds solution for the \emph{single source
shortest path problem} (SSSP) since these problems are special cases of the
considered problem.
