An approximation notion between P and FPTAS

TL;DR

This paper introduces a new approximation concept for NP-hard problems that is stronger than FPTAS but weaker than polynomial-time solvability, assuming P != NP.

Contribution

The authors define a novel approximation notion for NP-hard problems and establish its position relative to FPTAS and polynomial algorithms.

Findings

The new approximation notion is strictly stronger than FPTAS.

It is strictly weaker than having a polynomial-time algorithm.

Assuming P != NP, the notion delineates a new complexity boundary.

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.