  We consider self-stabilizing algorithms to compute a Maximal Independent Set
(MIS) in the extremely weak beeping communication model. The model consists of
an anonymous network with synchronous rounds. In each round, each vertex can
optionally transmit a signal to all its neighbors (beep). After the
transmission of a signal, each vertex can only differentiate between no signal
received, or at least one signal received. We assume that vertices have some
knowledge about the topology of the network.
  We revisit the not self-stabilizing algorithm proposed by Jeavons, Scott, and
Xu (2013), which computes an MIS in the beeping model. We enhance this
algorithm to be self-stabilizing, and explore two different variants, which
differ in the knowledge about the topology available to the vertices. In the
first variant, every vertex knows an upper bound on the maximum degree $\Delta$
of the graph. For this case, we prove that the proposed self-stabilizing
version maintains the same run-time as the original algorithm, i.e. it
stabilizes after $O(\log n)$ rounds w.h.p. on any $n$-vertex graph. In the
second variant, each vertex only knows an upper bound on its own degree. For
this case, we prove that the algorithm stabilizes after $O(\log n\cdot \log
\log n)$ rounds on any $n$-vertex graph, w.h.p.
