Online Non-Preemptive Scheduling to Minimize Weighted Flow-time on Unrelated Machines
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.
Online Algorithms
Scheduling
Resource Augmentation
Theory of computation~Scheduling algorithms
59:1-59:12
Regular Paper
Nguyen Kim Thang is supported by the ANR project OATA nsuperscript{o} ANR-15-CE40-0015-01, Hadamard PGMO and DIM RFSI. Abhinav Srivastav was supported by the PSL project Multi-Fac and is supported by the ANR project OATA nsuperscript{o} ANR-15-CE40-0015-01, Hadamard PGMO and DIM RFSI. Benjamin Moseley was supported in part by a Google Research Award, and NSF Grants CCF-1617724, CCF-1733873 and CCF-1725661.
Giorgio
Lucarelli
Giorgio Lucarelli
Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LIG, France
Benjamin
Moseley
Benjamin Moseley
Carnegie Mellon University, USA
Nguyen Kim
Thang
Nguyen Kim Thang
IBISC, Univ Evry, University Paris-Saclay, France
Abhinav
Srivastav
Abhinav Srivastav
IBISC, Univ Evry, University Paris-Saclay, France
Denis
Trystram
Denis Trystram
Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LIG, France
10.4230/LIPIcs.ESA.2018.59
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Giorgio Lucarelli, Benjamin Moseley, Nguyen Kim Thang, Abhinav Srivastav, and Denis Trystram
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