Constant-time distributed dominating set approximation

  • Authors:
  • Fabian Kuhn;Rogert Wattenhofer

  • Affiliations:
  • ETH Zurich, Zurich, Switzerland;ETH Zurich, Zurich, Switzerland

  • Venue:
  • Proceedings of the twenty-second annual symposium on Principles of distributed computing
  • Year:
  • 2003

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Abstract

Finding a small dominating set is one of the most fundamental problems of traditional graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary parameter k and maximum degree Δ, our algorithm computes a dominating set of expected size O(kΔ2/k log Δ|DSOPT|) in O(k2) rounds where each node has to send O(k2Δ) messages of size O(logΔ). This is the first algorithm which achieves a non-trivial approximation ratio in a constant number of rounds.