Maximum Job Size Research Articles

Competitively Scheduling Tasks with Intermediate Parallelizability

We introduce a scheduling algorithm Intermediate-SRPT, and show that it is O (log P )-competitive with respect to average flow time when scheduling jobs whose parallelizability is intermediate between being fully parallelizable and sequential. Here, the parameter P denotes the ratio between the maximum job size to the minimum. We also show a general matching lower bound on the competitive ratio. Our analysis builds on an interesting combination of potential function and local competitiveness arguments.

Several semi-online scheduling problems on two identical machines with combined information

In this paper we consider several semi-online scheduling problems on two identical machines with combined information. The objective of each problem is to minimize the makespan. The first problem is semi-online scheduling with known optimal solution value and maximum job size. We obtain a lower bound 65 and design an optimal algorithm with a competitive ratio 65. The second problem is semi-online scheduling with a buffer of size k, where k(k≥1) is a finite positive integer, and known maximum job size. We obtain a lower bound 65 and design an algorithm with a competitive ratio 54. The third problem is semi-online scheduling with a buffer of size 1 and jobs arriving in decreasing order of their processing times. We obtain a lower bound 76, which matches an upper bound in the literature. The last problem is semi-online scheduling with a buffer of size 1 and all the job processing times being bounded in the interval [1,t](t≥1). We obtain a lower bound max{min{43,t+26},min{54,t+14},min{76,t+23}}, where the lower bound 43 for t≥6 matches an upper bound in the literature, and design an algorithm with a competitive ratio max{t+23,87} for 1≤t≤32, which is optimal for 107≤t≤32.

Semi-online scheduling with known partial information about job sizes on two identical machines

In this paper we consider the semi-online scheduling problem with known partial information about job sizes on two identical machines, where all the jobs have processing times in the interval [ p , t p ] ( p > 0 , t ≥ 1 ) and the maximum job size is t p . The objective is to minimize the makespan. For 1 ≤ t < 4 3 and t ≥ 2 , we obtain lower bounds t + 1 2 and 4 3 on the optimal solution, respectively, which match the upper bounds given by He and Zhang (1999) in [2]. For 4 3 ≤ t < 2 , we prove that a lower bound on the optimal solution is max { 4 t + 4 3 t + 4 , 2 t t + 1 } and design an algorithm with a competitive ratio equal to this lower bound.

Improved multi-processor scheduling for flow time and energy

Energy usage has been an important concern in recent research on online scheduling. In this paper, we study the tradeoff between flow time and energy (Albers and Fujiwara in ACM Trans. Algorithms 3(4), 2007; Bansal et al. in Proceedings of ACM-SIAM Symposium on Discrete Algorithms, pp. 805---813, 2007b, Bansal et al. in Proceedings of International Colloquium on Automata, Languages and Programming, pp. 409---420, 2008; Lam et al. in Proceedings of European Symposium on Algorithms, pp. 647---659, 2008b) in the multi-processor setting. Our main result is an enhanced analysis of a simple non-migratory online algorithm called CRR (classified round robin) on m?2 processors, showing that its flow time plus energy is within O(1) times of the optimal non-migratory offline algorithm, when the maximum allowable speed is slightly relaxed. The result still holds even if the comparison is made against the optimal migratory offline algorithm. This improves previous analysis that CRR is O(log?P)-competitive where P is the ratio of the maximum job size to the minimum job size.

Semi-online scheduling with known maximum job size on two uniform machines

In this paper, we investigate the semi-online scheduling problem with known maximum job size on two uniform machines with the speed ratio s?1. The objective is to minimize the makespan. Two algorithms are presented, where the first is optimal for $1\leq s\leq\sqrt{2}$ , and the second is optimal for 1.559?s?2 and $s\ge \frac{3+\sqrt{17}}{2}$ . In addition, the improvement on lower bounds is made for $2 .

Nonmigratory Multiprocessor Scheduling for Response Time and Energy

Energy usage has been an important concern in recent research on online job scheduling, where processors are allowed to vary the speed dynamically so as to save energy whenever possible. Notice that providing good quality of service such as response time (flow time) and conserving energy are conflicting objectives. An interesting problem for scheduling is how to optimize an economic tradeoff of flow time and energy. To this end, the past two years have witnessed significant progress in the single-processor setting, and online algorithms with performance close to optimal have been obtained. In this paper we extend the study of optimizing the tradeoff between flow time and energy to the multi-processor setting. We derive and analyze a simple non-migratory online algorithm that makes use of the classified-round-robin (CRR) strategy to dispatch jobs. Even in the worst case, its performance is within O(log P) times of the optimal migratory offline algorithm, where P is the ratio of the maximum job size to the minimum job size. Technically speaking, this online result stems from a non-trivial solution to an offline problem of eliminating migration, which is also interesting by itself.