Constant-time distributed dominating set approximation

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., our algorithm computes a dominating set of expected size O (k Delta(2/k) log(Delta)vertical bar DSOPT vertical bar) in O (k(2)) rounds. Each node has to send O (k(2)Delta) messages of size O( log Delta). This is the first algorithm which achieves a non-trivial approximation ratio in a constant number of rounds.