Deterministic Distributed Dominating Set Approximation in the CONGEST Model

We develop deterministic approximation algorithms for the minimum dominating set problem in the CONGEST model with an almost optimal approximation guarantee. For ε 1/ poly log Δ we obtain two algorithms with approximation factor (1 + ε)(1 + ł n (Δ + 1)) and with runtimes 2O(√ log n log log n) and O(Δ poly log Δ + poly log Δ log* n), respectively. Further we show how dominating set approximations can be deterministically transformed into a connected dominating set in the CONGEST model while only increasing the approximation guarantee by a constant factor. This results in a deterministic O(log Δ)-approximation algorithm for the minimum connected dominating set with time complexity 2O(√ log n log log n).