In my dissertation, I focus on the dominating set in graphs. I have researched different algorithms to find the minimum dominating sets and their approximations. I have tested the algorithms on different graph models.
I have investigated the accuracy of various methods on various models of graphs and their time complexities.
With the simulations, I have confirmed the estimate for the accuracy of the greedy method, which I had previously proved theoretically. The estimate is very good for the Erdős--Rényi graph model. It also applies to the Barabási--Albert model, although a lower upper bound could be obtained for this kind of graphs.