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