Schedules with a single preemption on uniform parallel machines

Soper, Alan; Strusevich, Vitaly A.

doi:10.1016/j.dam.2018.03.007

Cited by 10 publications

(15 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Soper and Strusevich (2018) prove that finding an optimal schedule with at most one preemption on two unrelated parallel machines is NP-hard. On the other hand, it is shown by Soper and Strusevich (2018) that on two uniform machines an optimal schedule with at most one preemption can be found in polynomial time; we reproduce the corresponding algorithm in Sect. 2.2.…”

Section: Introductionmentioning

confidence: 98%

“…For m ≥ 3 uniform machines, the problem of finding an optimal schedule with the number of preemptions q such that q is even and q ≤ 2 (m − 3) is shown to be NP-hard by Shachnai et al (2005). Soper and Strusevich (2018) prove that finding an optimal schedule with at most one preemption on two unrelated parallel machines is NP-hard. On the other hand, it is shown by Soper and Strusevich (2018) that on two uniform machines an optimal schedule with at most one preemption can be found in polynomial time; we reproduce the corresponding algorithm in Sect.…”

Section: Introductionmentioning

confidence: 99%

“…According to Woeginger (2000), for m uniform parallel machines ρ (0) m = 2 − 1/m. In Soper and Strusevich (2014b), the necessary and sufficient conditions under which the global bound of 2 − 1/m is tight are given. If the makespan of an optimal preemptive schedule S * p is equal to the ratio of the total processing time of r < m longest jobs over the total speed of r fastest machines, it is shown in Soper and Strusevich (2014b) that the tight bound on the power of preemption ρ (0)…”

Section: Introductionmentioning

confidence: 99%

“…For identical machines, Braun and Schmidt (2003) prove that ρ (q) m = (2m) / (m + q + 1), where 0 ≤ q ≤ m − 1, and that this bound is tight. For the problem on m uniform parallel machines, Soper and Strusevich (2018) show that ρ (1) Jiang et al (2014) perform a parametric analysis of a single preemption for two uniform machines with speeds s and s , where s ≥ s , from which it follows that…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we focus on the problem on three uniform parallel machines. The bound ρ (1) 3 = 4 3 follows from Soper and Strusevich (2018) and holds as a global bound for all instances, irrespective of relative speeds of the machines. The main purpose of this paper is to perform a parametric analysis of the value ρ (1) 3 .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Parametric analysis of the quality of single preemption schedules on three uniform parallel machines

Soper

Strusevich

2018

Ann Oper Res

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Parametric analysis of the quality of single preemption schedules on three uniform parallel machines

Soper

Strusevich

2018

Ann Oper Res

Self Cite

View full text Add to dashboard Cite

show abstract

Three notes on scheduling unit-length jobs with precedence constraints to minimize the total completion time

Wang

Bellenguez

2021

J Sched

View full text Add to dashboard Cite

In this paper, we provide three notes on scheduling unit-length jobs with precedence constraints to minimize the total completion time. First, we propose an exact algorithm for in-trees, of which the complexity depends mainly on the graph height, i.e., the length of the longest chain of the precedence graph. We show that this work improves the algorithm in the literature both theoretically and experimentally. Second, we close the open problem for level-orders by showing how it is polynomially solvable. Third, we prove that preemptive scheduling in-trees is strongly NP-hard with arbitrary number of machines, of which the complexity was also open.

show abstract

Preemptive and non-preemptive scheduling on two unrelated parallel machines

Soper

Strusevich

2022

J Sched

Self Cite

View full text Add to dashboard Cite

In this paper, for the problem of minimizing the makespan on two unrelated parallel machines we compare the quality of preemptive and non-preemptive schedules.It is known that there exists an optimal preemptive schedule with at most two preemptions. We show that the power of preemption, i.e., the ratio of the makespan computed for the best non-preemptive schedule to the makespan of the optimal preemptive schedule is at most 3/2. We also show that the ratio of the makespan computed for the best schedule with at most one preemption to the makespan of the optimal preemptive schedule is at most 9/8. For both models, we present polynomial-time algorithms that find schedules of the required quality. The established bounds match those previously known for a less general problem with two uniform machines. We have found one point of difference between the uniform and unrelated machines: if an optimal preemptive schedule contains exactly one preemption then the ratio of the makespan computed for the best non-preemptive schedule to the makespan of the optimal preemptive schedule is at most 4/3 if the two machines are uniform and remains 3/2 if the machines are unrelated.

show abstract

Schedules with a single preemption on uniform parallel machines

Cited by 10 publications

References 15 publications

Parametric analysis of the quality of single preemption schedules on three uniform parallel machines

Parametric analysis of the quality of single preemption schedules on three uniform parallel machines

Three notes on scheduling unit-length jobs with precedence constraints to minimize the total completion time

Preemptive and non-preemptive scheduling on two unrelated parallel machines

Contact Info

Product

Resources

About