An EPTAS for Machine Scheduling with Bag-Constraints

Grage, Kilian; Jansen, Klaus; Klein, Kim-Manuel

doi:10.1145/3323165.3323192

Cited by 13 publications

(7 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This problem was already studied in the 1990's (see e.g. [6,7]), and there has been a series of recent results [10,15,28] regarding the setting corresponding to MSRS where the conflict graph is a collection of disjoint cliques.…”

Section: State Of the Art And Motivationmentioning

confidence: 99%

Scheduling with Many Shared Resources

Deppert¹,

Jansen²,

Maack³

et al. 2022

Preprint

View full text Add to dashboard Cite

Consider the many shared resource scheduling problem where jobs have to be scheduled on identical parallel machines with the goal of minimizing the makespan. However, each job needs exactly one additional shared resource in order to be executed and hence prevents the execution of jobs that need the same resource while being processed. Previously a (2m/(m + 1))-approximation was the best known result for this problem. Furthermore, a 6/5-approximation for the case with only two machines was known as well as a PTAS for the case with a constant number of machines. We present a simple and fast 5/3-approximation and a much more involved but still reasonable 1.5-approximation. Furthermore, we provide a PTAS for the case with only a constant number of machines, which is arguably simpler and faster than the previously known one, as well as a PTAS with resource augmentation for the general case. The approximation schemes make use of the N-fold integer programming machinery, which has found more and more applications in the field of scheduling recently. It is plausible that the latter results can be improved and extended to more general cases. Lastly, we give a 5/4 − ε inapproximability result for the natural problem extension where each job may need up to a constant number (in particular 3) of different resources.

show abstract

Section: State Of the Art And Motivationmentioning

confidence: 99%

Scheduling with Many Shared Resources

Deppert¹,

Jansen²,

Maack³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…They also provided an 8-approximate algorithm for unrelated machines with additional constraints. This approach was further pursued in Grage, Jansen, and Klein (2019), where an EPTAS for identical machines case was presented. The last result is a construction of a PTAS for uniform machines with some additional restrictions on machine speeds and bag sizes (Page and Solis-Oba 2020).…”

Section: An Overview Of the Previous Workmentioning

confidence: 99%

Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines

Pikies

Turowski

Kubale

2021

ICAPS

View full text Add to dashboard Cite

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

“…They also provided an 8-approximate algorithm for unrelated machines with additional constraints. This approach was further pursued in [18], where an EPTAS for identical machines case was presented. The last result is a construction of PTAS for uniform machines with some additional restrictions on machine speeds and bag sizes [19].…”

Section: An Overview Of Previous Workmentioning

confidence: 99%

Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines

Pikies¹,

Turowski²,

Kubale³

2020

Preprint

View full text Add to dashboard Cite

In this paper we consider the problem of 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. Our research stems from the work of Bodlaender et al. [1], [2]. In particular, we pursue the line investigated partially by Mallek et al. [3], where the graph is complete multipartite so each machine can do jobs only from one partition.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 easy problems, or algorithms with a guaranteed constant worst-case approximation ratio or even in some cases a PTAS for the harder ones.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

An EPTAS for Machine Scheduling with Bag-Constraints

Cited by 13 publications

References 11 publications

Scheduling with Many Shared Resources

Scheduling with Many Shared Resources

Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines

Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines

Contact Info

Product

Resources

About