Near-optimal distributed dominating set in bounded arboricity graphs

Abstract We describe a simple deterministic $$O( \varepsilon ^{-1} \log \Delta )$$ O ( ε - 1 log Δ ) round distributed algorithm for $$(2\alpha +1)(1 + 2 α + approximation of minimum weighted dominating set on graphs with arboricity at most $$\alpha $$ . Here $$\Delta denotes the maximum degree. also show lower bound proving that this complexity is nearly optimal even unweighted case, via reduction from celebrated KMW vertex cover (Kuhn et al. in JACM 63:116, 2016). Our improves all previous results (that work only graphs) including randomized $$O(\alpha ^2)$$ $$O(\log n)$$ n rounds (Lenzen International symposium computing, Springer, 2010), international ^2 (implicit Bansal Inform Process Lett 122:21–24, 2017; Proceeding 17th discrete algorithms (SODA), 2006), and (Morgan 35th symposiumon 2021). provide sharpens factor to (1+o(1))$$ o If each node restricted do polynomial-time computations, our tight first order as it NP-hard achieve - 1 (Bansal 122:21-24, 2017).