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In research on distributed local algorithms it is commonly assumed that eachvertex has a unique identifier in the entire graph. However, it turns out thatin case of certain classes of graphs (for example not lift-closed boundeddegree 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 whichreturns constant approximation of the MDS problem in CONGEST model. Thealgorithm doesn't use any additional information about the structure of thegraph and the nodes don't have unique identifiers. We hope that this paper willbe very helpful as a hint for further comparisons of the unique identifiermodel and the model with only a port numbering in other classes of graphs.

A local constant-factor approximation algorithm for MDS problem in anonymous network