🤖 AI Summary
This work addresses the approximability of NP-hard optimization problems by introducing a novel approximation notion that characterizes the intermediate approximability of problems defined via binary functions—situating them between polynomial-time solvability and the existence of a fully polynomial-time approximation scheme (FPTAS). Under the standard assumption that P ≠ NP, the authors rigorously establish through formal reductions and complexity-theoretic analysis that this newly defined approximation hierarchy is strictly stronger than FPTAS yet strictly weaker than polynomial-time solvability. This result fills a critical gap in the theory of approximation algorithms and offers a refined perspective on the boundary of approximability for NP-hard problems.
📝 Abstract
We present an approximation notion for NP-hard optimization problems represented by binary functions. We prove that (assuming P != NP) the new notion is strictly stronger than FPTAS, but strictly weaker than having a polynomial-time algorithm.