Semi-on-line problems on two identical machines with combined partial information

Tan, Zhiyi; He, Yong

doi:10.1016/s0167-6377(02)00164-5

Cited by 48 publications

(18 citation statements)

References 11 publications

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“…Some combination of the previous restrictions were studied in [14] for non-preemptive scheduling on identical machines. We should note that there are also semi-online models that do not fit into our framework at all.…”

Section: Semi-online Restrictions and Previous Workmentioning

confidence: 99%

Semi-Online Preemptive Scheduling: One Algorithm for All Variants

Ebenlendr

Sgall

2010

Theory Comput Syst

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Abstract. We present a unified optimal semi-online algorithm for preemptive scheduling on uniformly related machines with the objective to minimize the makespan. This algorithm works for all types of semi-online restrictions, including the ones studied before, like sorted (decreasing) jobs, known sum of processing times, known maximal processing time, their combinations, and so on. Based on the analysis of this algorithm, we derive some global relations between various semi-online restrictions and tight bounds on the approximation ratios for a small number of machines.

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Section: Semi-online Restrictions and Previous Workmentioning

confidence: 99%

Semi-Online Preemptive Scheduling: One Algorithm for All Variants

Ebenlendr

Sgall

2010

Theory Comput Syst

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“…Various other models of semi-online scheduling problems on identical machines have been studied extensively in recent years [11,16,10,13,2,6,15,3,12]. These variants differ in which partial information about future job is known in advance.…”

Section: Previous Workmentioning

confidence: 99%

Semi-online scheduling with “end of sequence” information

Epstein

2007

J Comb Optim

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We study a variant of classical scheduling, which is called scheduling with "end of sequence" information. It is known in advance that the last job has the longest processing time. Moreover, the last job is marked, and thus it is known for every new job whether it is the final job of the sequence. We explore this model on two uniformly related machines, that is, two machines with possibly different speeds. Two objectives are considered, maximizing the minimum completion time and minimizing the maximum completion time (makespan). Let s be the speed ratio between the two machines, we consider the competitive ratios which are possible to achieve for the two problems as functions of s. We present algorithms for different values of s and lower bounds on the competitive ratio. The proposed algorithms are best possible for a wide range of values of s. For the overall competitive ratio, we show tight bounds of φ + 1 ≈ 2.618 for the first problem, and upper and lower bounds of 1.5 and 1.46557 for the second problem.

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“…Epstein (2003) considers the case in which the optimal solution value is known and the jobs arrive in non-increasing order of their processing times, and provides an optimal algorithm with a competitive ratio 10 9 . Tan et al (2002) consider two semi-online scheduling problems with combined information. One is that the total processing time of all the jobs is known and the jobs arrive in non-increasing order of their processing times.…”

Section: Introductionmentioning

confidence: 99%

Semi-online scheduling with combined information on two identical machines in parallel

Cao

Wan

2014

J Comb Optim

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This paper is concerned with a semi-online scheduling problem with combined information on two identical parallel machines to minimize the makespan, where all the jobs have processing times in the interval [1, t] (t ≥ 1) and the jobs arrive in non-increasing order of their processing times. The objective is to minimize the makespan. For t ≥ 1, we obtain a lower bound max N =1,2,3,... min{ 4N +3 4N +2 , N t+N +1 2N +1 } and show that the competitive ratio of the L S algorithm achieves the lower bound.

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Semi-on-line problems on two identical machines with combined partial information

Cited by 48 publications

References 11 publications

Semi-Online Preemptive Scheduling: One Algorithm for All Variants

Semi-Online Preemptive Scheduling: One Algorithm for All Variants

Semi-online scheduling with “end of sequence” information

Semi-online scheduling with combined information on two identical machines in parallel

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