Approximation Schemes for Machine Scheduling

In this paper we consider a problem of job scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine. We provide several results concerning schedules, optimal or approximate with respect to the two most popular criteria of optimality: Cmax (makespan) and ∑Cj (total completion time). We consider a variety of machine types in our paper: identical, uniform, and unrelated. Our results consist of delimitation of the easy (polynomial) and NP-hard problems within these constraints. We also provide algorithms, either polynomial exact algorithms for the easier problems, or algorithms with a guaranteed constant worst-case approximation ratio. In particular, we fill the gap on research for the problem of finding a schedule with the smallest ∑Cj on uniform machines. We address this problem by developing a linear programming relaxation technique with an appropriate rounding, which to our knowledge is a novelty for this criterion in the considered setting.

show abstract

Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines

Pikies

Turowski

Kubale

2021

ICAPS

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Approximation Schemes for Machine Scheduling

Cited by 1 publication

References 115 publications

Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines

Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines

Contact Info

Product

Resources

About