The Largest-Z-ratio-First algorithm is 0.8531-approximate for scheduling unreliable jobs on m parallel machines

TL;DR

This paper analyzes the Largest-Z-ratio-First greedy algorithm for scheduling unreliable jobs on parallel machines, proving it achieves a tight approximation ratio of approximately 0.8531 for maximizing expected reward.

Contribution

The paper provides a tight analysis of the Largest-Z-ratio-First algorithm's worst-case performance for scheduling unreliable jobs, establishing a specific approximation ratio.

Findings

Approximation ratio of about 0.853196 for the algorithm

The bound is proven to be tight

Analysis applies to scheduling on m parallel machines

Abstract

In this paper we analyze the worst-case performance of a greedy algorithm called Largest-Z-ratio-First for the problem of scheduling unreliable jobs on m parallel machines. Each job is characterized by a success probability and a reward earned in the case of success. In the case of failure, the jobs subsequently sequenced on that machine cannot be performed. The objective is to maximize the expected reward. We show the algorithm provides an approximation ratio of approximately 0.853196, and that the bound is tight.