Fully Polynomial Time Approximation Scheme

A Fully Polynomial Time Approximation Scheme (FPTAS) is an algorithmic approach designed to find near-optimal solutions for complex problems efficiently. It guarantees solutions within a user-defined small margin of error (say, within 1% of the best possible). The "fully polynomial" aspect means that the time it takes to find this approximate solution increases polynomially with both the size of the input and the inverse of the error margin, ensuring it remains practical even for large problems. Essentially, FPTAS balances accuracy and efficiency, providing good solutions quickly when exact solutions are computationally hard to obtain.