A best online algorithm for unbounded parallel-batch scheduling with restarts to minimize makespan

Online Scheduling with Delivery Time on a Bounded Parallel Batch Machine with Limited Restart

“…While using restarts, a best possible online algorithm with a competitive ratio of 3/2 was given in Akker et al [2]. Other researches with restarts can see Epstein and Stee [3], Stee and Poutré [4], and Yuan et al [5].…”

“…For the problem of minimizing makespan on an unbounded parallel batch machine with restarts, Fu et al [19] showed that any online algorithm cannot have a competitive ratio of less than (5 − √ 5)/2 and Yuan et al [5] gave a best possible online algorithm matching the lower bound. For the corresponding problem using limited restart, Fu et al [6] gave an online algorithm with a competitive ratio of 3/2 and proved that it is best possible.…”

Online Over Time Scheduling on Parallel-Batch Machines: A Survey

“…They proved that no online algorithm has a competitive ratio less than 5À ffiffi 5 p 2 , and they presented a 3 2competitive algorithm. Later, Yuan et al [49] designed a best possible online algorithm with a competitive ratio 5À ffiffi 5 p 2 . Fu et al [15] studied the same problem with limited restarts, in which a job cannot be restarted twice.…”

“…on the competitive ratio of any online algorithm, then they provided an online algorithm H m ðhÞ with a parameter 0\h\1 , and showed that its competitive ratio is no less than 1 þ ffiffiffi ffi Furthermore, for problem 1jonline; p-batch; b\1jC max , the known lower bound is 1.618 and the known upper bound is 2. Poon and Yu [36] presented an online [14,49] 1jonline; p-batch; b ¼ 1; L-restartjC max 1:5 1 :5 [ 15] 1jonline; p-batch;…”

Online scheduling on two parallel-batching machines with limited restarts to minimize the makespan

“…doi:10.1016/j.ipl.2010.04.008 researchers have studied this problem in both the off-line and online environments, e.g., Brucker et al [1], Lee and Uzsoy [5], and Poon and Zhang [9], to name a few. Yuan et al [11] investigated online scheduling on a parallelbatching machine with restarts to minimize the makespan. They provided a best possible online algorithm with a competitive ratio 5− √ 5 2 .…”