Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

An approximation notion between P and FPTAS

Samuel Bismuth, Erel Segal-Halevi

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.

An approximation notion between P and FPTAS

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.
Paper Structure (10 sections, 3 theorems, 3 equations)

This paper contains 10 sections, 3 theorems, 3 equations.

Table of Contents

  1. Introduction
  2. Motivation
  3. Definitions
  4. Main theorem
  5. Proof of part (1)
  6. Proof of part (2)
  7. Proof of part (3)
  8. Proof of part (4)
  9. Is FFPTAS a new complexity class?
  10. Not Every Polynomial-time Solvable Problem is Relaxable

Key Result

Theorem 5

The following hold among the class of relaxable maximization problems: (1) If a relaxable problem has a polynomial-time algorithm, then it also has an FFPTAS. (2) Some relaxable problem has an FFPTAS but no polytime algorithm unless P$=$NP. (3) If a relaxable problem has an FFPTAS, then it also has

Theorems & Definitions (15)

  • Definition 1
  • Definition 2
  • Definition 3
  • Remark 4
  • Theorem 5
  • Claim
  • Remark 6
  • Claim
  • Remark 7
  • Claim
  • ...and 5 more