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arXiv · 1905.10775

Deterministic Distributed Dominating Set Approximation in the CONGEST Model

Janosch Deurer·Fabian Kuhn·Yannic Maus
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Abstract

We develop deterministic approximation algorithms for the minimum dominating set problem in the CONGEST model with an almost optimal approximation guarantee. For $\epsilon>1/{\text{{poly}}}\log \Delta$ we obtain two algorithms with approximation factor $(1+\epsilon)(1+\ln (\Delta+1))$ and with runtimes $2^{O(\sqrt{\log n \log\log n})}$ and $O(\Delta\cdot\text{poly}\log \Delta +\text{poly}\log \Delta \log^{*} n)$, 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 $O(\log \Delta)$-approximation algorithm for the minimum connected dominating set with time complexity $2^{O(\sqrt{\log n \log\log n})}$.

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Janosch Deurer, Fabian Kuhn, Yannic Maus. 2019-05-26. Deterministic Distributed Dominating Set Approximation in the CONGEST Model. https://arxiv.org/abs/1905.10775

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