The exploration and categorization of essential and synthetic lethality genes hold significant importance in seeking effective and targeted therapies for diverse ailments. This endeavor hinges upon genetic minimal cut sets (gMCSs), which also find utility in metabolic engineering. There have been various methods suggested for calculating gMCSs. Still, with the emergence of numerous new models and their growing intricacy, it has become vital to introduce new algorithms in this field. This paper presents a new algorithmic approach for computing gMCSs, which utilizes linear programming techniques to improve temporal efficiency. The key concept of the method is to use a k-representative subset to replace the target set with a smaller one.