Scheduling on identical machines: How good is LPT in an on-line setting?

Chen, Bo; Vestjens, Arjen P. A.

doi:10.1016/s0167-6377(97)00040-0

Cited by 86 publications

(38 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…B 1 , B 2 , B 3 , B 4 are the last four batches. Note that the starting time of B 1 , B 2 , B 3 are all before r (4) , where r (4) is the arrival time of the longest job in B 4 . Furthermore, the starting time of B 1 is before that of B 2 , which is before that of B 3 , while the starting time of B 4 is equal to max{C 3 , (1 + β)r (4) + βp (4) }, which is C 3 in our example.…”

Section: Algorithm Dp H(β)mentioning

confidence: 99%

On‐line algorithms for minimizing makespan on batch processing machines

Zhang

Cai

Wong

2001

Naval Research Logistics

View full text Add to dashboard Cite

Abstract:We consider the problem of scheduling jobs on-line on batch processing machines with dynamic job arrivals to minimize makespan. A batch processing machine can handle up to B jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. In the first part of this paper, we address the single batch processing machine scheduling problem. First we deal with two variants: the unbounded model where B is sufficiently large and the bounded model where jobs have two distinct arrival times. For both variants, we provide on-line algorithms with worst-case ratio ( √ 5 + 1)/2 (the inverse of the Golden ratio) and prove that these results are the best possible. Furthermore, we generalize our algorithms to the general case and show a worst-case ratio of 2. We then consider the unbounded case for parallel batch processing machine scheduling. Lower bounds are given, and two on-line algorithms are presented.

show abstract

Section: Algorithm Dp H(β)mentioning

confidence: 99%

On‐line algorithms for minimizing makespan on batch processing machines

Zhang

Cai

Wong

2001

Naval Research Logistics

View full text Add to dashboard Cite

show abstract

“…In the one-by-one model competitive ratios increase with increasing number of machines. In real time online scheduling nobody has been able to show smaller competitive ratios for multiple machine problems than for the single machine versions, though here lower bounds do not exclude that such results exist (and indeed people suspect they do) [8,9].…”

Section: Introductionmentioning

confidence: 84%

Online k-Server Routing Problems

Bonifaci

Stougie

2008

Theory Comput Syst

View full text Add to dashboard Cite

Abstract.In an online k-server routing problem, a crew of k servers has to visit points in a metric space as they arrive in real time. Possible objective functions include minimizing the makespan (k-Traveling Salesman Problem) and minimizing the average completion time (k-Traveling Repairman Problem). We give competitive algorithms, resource augmentation results and lower bounds for k-server routing problems on several classes of metric spaces. Surprisingly, in some cases the competitive ratio is dramatically better than that of the corresponding single server problem. Namely, we give a 1 + O((log k)/k)-competitive algorithm for the k-Traveling Salesman Problem and the k-Traveling Repairman Problem when the underlying metric space is the real line. We also prove that similar results cannot hold for the Euclidean plane.

show abstract

“…In the one-by-one model competitive ratios increase with increasing number of machines. In real time on-line scheduling nobody has been able to show smaller competitive ratios for multiple machine problems than for the single machine versions, but here lower bounds do not exclude that such results exist [16,17,43]. Actually, the multiple machine problems get quite hard to analyze so that often the lower bounds are lower, and the upper bounds higher, than the single server case.…”

Section: Theorem 15 ([14]mentioning

confidence: 99%