  In research on distributed local algorithms it is commonly assumed that each
vertex has a unique identifier in the entire graph. However, it turns out that
in case of certain classes of graphs (for example not lift-closed bounded
degree graphs) identifiers are unnecessary and only a port ordering is needed.
One of the open issues was whether identifiers are essential in planar graphs.
In this paper, we answer this question and we propose an algorithm which
returns constant approximation of the MDS problem in CONGEST model. The
algorithm doesn't use any additional information about the structure of the
graph and the nodes don't have unique identifiers. We hope that this paper will
be very helpful as a hint for further comparisons of the unique identifier
model and the model with only a port numbering in other classes of graphs.
