This paper studies the construction of self-stabilizing topologies for distributed systems. While recent research has focused on chain topologies where nodes need to be linearized with respect to their identifiers, we go a step further and explore a natural 2-dimensional generalization. In particular, we present a local self-stabilizing algorithm that constructs a Delaunay graph from any initial connected topology and in a distributed manner. This algorithm terminates in time O(n3) in the worst-case. We believe that such self-stabilizing Delaunay networks have interesting applications and give insights into the necessary geometric reasoning that is required for higher-dimensional linearization problems.

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