Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs

Abstract

We prove a large deviation principle for a greedy exploration process on an Erdös-Rényi (ER) graph when the number of nodes goes to infinity. To prove our main result, we use the general strategy to study large deviations of processes proposed by Feng and Kurtz (2006), 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 large deviation trajectory. Also, we derive large deviation results for the size of the maximum independent set discovered by such an algorithm and analyse the probability that it exceeds known bounds for the maximal independent set. We also analyse the link between these results and the landscape complexity of the independent set and the exploration dynamic