An estimation of the greedy algorithm's accuracy for a set cover problem instance

Considering the set cover problem, by modifying the approach that gives a logarithmic approximation guarantee for the greedy algorithm, we obtain an estimation of the greedy algorithm’s accuracy for a particular input. We compare the presented estimation to another estimations of this type. We give such examples of the set cover problem instances that the presented estimation sagnificantly improves over linear programming relaxation based estimation.