The Set Covering Problem (SCP) is a fundamental combinatorial optimization problem with a lot of applications in fields like operations research and logistics. This paper introduces two enhanced greedy algorithms to address SCP: the Improved Greedy Algorithm (IGA) and the Set-Based Greedy Algorithm (SGA). These algorithms enhance the classical greedy approach with novel heuristics for better item set selection and optimization. Experiments using benchmark datasets demonstrate that SGA consistently achieves higher solution quality at the cost of increased computation time, while IGA offers a balance between solution quality and computational efficiency. Comparative analysis highlights the suitability of each algorithm for different problem complexities, suggesting their potential for integration into hybrid optimization frameworks.