Polynomial time approximation scheme (PTAS)

A Polynomial Time Approximation Scheme (PTAS) is a method for solving difficult optimization problems. It produces solutions close to the best possible (optimal) answer, within a small, adjustable margin of error. The "polynomial time" aspect means the time it takes grows reasonably with the problem size, making it feasible for large instances. Essentially, PTAS allows us to find nearly optimal solutions efficiently, with the flexibility to balance accuracy and computation time based on how close we want the answer to be to the perfect solution.