Analysis of Busy-Time Scheduling on Heterogeneous Machines

TL;DR

This paper introduces algorithms for efficiently scheduling jobs on heterogeneous machines to minimize total costs, considering machine capacities and job time intervals, with proven approximation guarantees.

Contribution

It presents the first asymptotically optimal approximation algorithms for busy-time scheduling on heterogeneous machines in both offline and online settings.

Findings

Developed an $O(1)$-approximation algorithm for offline scheduling.

Designed an $O(mu)$-competitive online algorithm.

Proved the algorithms' asymptotic optimality.

Abstract

This paper studies a generalized busy-time scheduling model on heterogeneous machines. The input to the model includes a set of jobs and a set of machine types. Each job has a size and a time interval during which it should be processed. Each job is to be placed on a machine for execution. Different types of machines have distinct capacities and cost rates. The total size of the jobs running on a machine must always be kept within the machine's capacity, giving rise to placement restrictions for jobs of various sizes among the machine types. Each machine used is charged according to the time duration in which it is busy, i.e., it is processing jobs. The objective is to schedule the jobs onto machines to minimize the total cost of all the machines used. We develop an $O(1)$-approximation algorithm in the offline setting and an $O(\mu)$-competitive algorithm in the online setting (where $\mu$ is the max/min job length ratio), both of which are asymptotically optimal.