Simultaneous approximation for scheduling problems

TL;DR

This paper introduces the concepts of strong and weak simultaneous approximation ratios to evaluate how well a single schedule can approximate all feasible schedules across various scheduling environments.

Contribution

It defines SAR and WAR and analyzes their properties in different scheduling settings, providing a new framework for approximation in scheduling problems.

Findings

SAR and WAR are characterized for various environments.

The paper establishes bounds for SAR and WAR in different scheduling models.

It offers insights into the feasibility of universal scheduling approximations.

Abstract

Motivated by the problem to approximate all feasible schedules by one schedule in a given scheduling environment, we introduce in this paper the concepts of strong simultaneous approximation ratio (SAR) and weak simultaneous approximation ratio (WAR). Then we study the two parameters under various scheduling environments, such as, non-preemptive, preemptive or fractional scheduling on identical, related or unrelated machines.