On Constant Time Approximation of Parameters of Bounded Degree Graphs

How well can the maximum size of an independent set, or the minimum size of a dominating set of a graph in which all degrees are at most d be approximated by a randomized constant time algorithm ? Motivated by results and questions of Nguyen and Onak, and of Parnas, Ron and Trevisan, we show that the best approximation ratio that can be achieved for the first question (independence number) is between Ω(d/ log d) and O(d log log d/ log d), whereas the answer to the second (domination number) is (1 + o(1)) ln d.