eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-14
59:1
59:12
10.4230/LIPIcs.ESA.2018.59
article
Online Non-Preemptive Scheduling to Minimize Weighted Flow-time on Unrelated Machines
Lucarelli, Giorgio
1
Moseley, Benjamin
2
Thang, Nguyen Kim
3
Srivastav, Abhinav
3
Trystram, Denis
1
Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LIG, France
Carnegie Mellon University, USA
IBISC, Univ Evry, University Paris-Saclay, France
In this paper, we consider the online problem of scheduling independent jobs non-preemptively so as to minimize the weighted flow-time on a set of unrelated machines. There has been a considerable amount of work on this problem in the preemptive setting where several competitive algorithms are known in the classical competitive model. However, the problem in the non-preemptive setting admits a strong lower bound. Recently, Lucarelli et al. presented an algorithm that achieves a O(1/epsilon^2)-competitive ratio when the algorithm is allowed to reject epsilon-fraction of total weight of jobs and has an epsilon-speed augmentation. They further showed that speed augmentation alone is insufficient to derive any competitive algorithm. An intriguing open question is whether there exists a scalable competitive algorithm that rejects a small fraction of total weights.
In this paper, we affirmatively answer this question. Specifically, we show that there exists a O(1/epsilon^3)-competitive algorithm for minimizing weighted flow-time on a set of unrelated machine that rejects at most O(epsilon)-fraction of total weight of jobs. The design and analysis of the algorithm is based on the primal-dual technique. Our result asserts that alternative models beyond speed augmentation should be explored when designing online schedulers in the non-preemptive setting in an effort to find provably good algorithms.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol112-esa2018/LIPIcs.ESA.2018.59/LIPIcs.ESA.2018.59.pdf
Online Algorithms
Scheduling
Resource Augmentation