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 Δ, our algorithm computes a dominating set of expected size O(kΔ2/k log (Δ)|DSOPT|) in O (K2) rounds. Each node has to send O(k2 Δ) messages of size O(log Δ). This is the first algorithm which achieves a non-trivial approximation ratio in a constant number of rounds.