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We prove a large deviation principle for the greedy exploration ofconfiguration models, building on a time-discretized version of the methodproposed by Bermolen et al. and Brightwell et al. for jointly constructing arandom graph from a given degree sequence and its exploration. The proof ofthis result follows the general strategy to study large deviations of processesproposed by Feng and Kurtz, based on the convergence of non-linear semigroups.We provide an intuitive interpretation of the LD cost function using Cramer'stheorem for the average of random variables with appropriate distribution,depending on the degree distribution of explored nodes. The rate function canbe expressed in a closed-form formula, and the large deviations trajectoriescan be obtained through explicit associated optimization problems. We thendeduce large deviations results for the size of the independent set constructedby the algorithm. As a particular case, we analyze these results for d-regulargraphs.

Large deviations for the greedy exploration process on configuration models