Large Deviation Principle for the Greedy Exploration Algorithm over Erdös-Rényi Graphs

We prove a large deviation principle (LDP) for a greedy exploration process on an Erdos-Renyi (ER) graph when the number of nodes goes to this http URL prove our main result we use the general strategy for the study of large deviations of processes proposed by Feng and Kurtz (2006), which is based on the convergence of non-linear semigroups. The rate function can be expressed in a closed form formula and associated optimization problems can be solved explicitly providing the trajectory of the large deviation. In addition we derive a LDP for the size of the maximum independent set discovered by such algorithm and analyze the probability that it exceeds known bounds for the maximal independent set. We also analyze the link between these results and the landscape complexity of the independent set and the exploration dynamic.