Constant-time distributed dominating set approximation

Abstract.Finding a small dominating set is one of the most fundamental problems of classical graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary, possibly constant parameter k and maximum node degree $\Delta$, our algorithm computes a dominating set of expected size ${\rm O}(k\Delta^{2/k}{\rm log}(\Delta)\vert DS_{\rm {OPT}}\vert)$ in ${\rm O}{(k^2)}$ rounds. Each node has to send ${\rm O}{(k^2\Delta)}$ messages of size ${\rm O}({\rm log}\Delta)$. This is the first algorithm which achieves a non-trivial approximation ratio in a constant number of rounds.