The competitiveness of on-line assignments
Journal of Algorithms
Flow and stretch metrics for scheduling continuous job streams
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Improved algorithms for stretch scheduling
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Server scheduling in the Lp norm: a rising tide lifts all boat
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Online scheduling to minimize the maximum delay factor
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Meeting deadlines: how much speed suffices?
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Resource augmentation for weighted flow-time explained by dual fitting
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
An online scalable algorithm for minimizing lk-norms of weighted flow time on unrelated machines
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On-line scheduling to minimize max flow time: an optimal preemptive algorithm
Operations Research Letters
| Hi-index | 0.00 |
We initiate the study of job scheduling on related and unrelated machines so as to minimize the maximum flow time or the maximum weighted flow time (when each job has an associated weight). Previous work for these metrics considered only the setting of parallel machines, while previous work for scheduling on unrelated machines only considered Lp, p 1 We give an O(ε−3)-competitive algorithm to minimize maximum weighted flow time on related machines where we assume that the machines of the online algorithm can process 1+ε units of a job in 1 time-unit (ε speed augmentation). 2 For the objective of minimizing maximum flow time on unrelated machines we give a simple 2/ε-competitive algorithm when we augment the speed by ε. For m machines we show a lower bound of Ω(m) on the competitive ratio if speed augmentation is not permitted. Our algorithm does not assign jobs to machines as soon as they arrive. To justify this "drawback" we show a lower bound of Ω(logm) on the competitive ratio of immediate dispatch algorithms. In both these lower bound constructions we use jobs whose processing times are in $\left\{1,\infty\right\}$, and hence they apply to the more restrictive subset parallel setting. 3 For the objective of minimizing maximum weighted flow time on unrelated machines we establish a lower bound of Ω(logm)-on the competitive ratio of any online algorithm which is permitted to use s=O(1) speed machines. In our lower bound construction, job j has a processing time of pj on a subset of machines and infinity on others and has a weight 1/pj. Hence this lower bound applies to the subset parallel setting for the special case of minimizing maximum stretch.