Online Makespan Minimization: The Power of Restart

Authors Zhiyi Huang, Ning Kang, Zhihao Gavin Tang, Xiaowei Wu, Yuhao Zhang

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Author Details

Zhiyi Huang
  • Department of Computer Sicence, The University of Hong Kong, Hong Kong
Ning Kang
  • Department of Computer Sicence, The University of Hong Kong, Hong Kong
Zhihao Gavin Tang
  • Department of Computer Sicence, The University of Hong Kong, Hong Kong
Xiaowei Wu
  • Department of Computing, The Hong Kong Polytechnic University, Hong Kong
Yuhao Zhang
  • Department of Computer Sicence, The University of Hong Kong, Hong Kong

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Zhiyi Huang, Ning Kang, Zhihao Gavin Tang, Xiaowei Wu, and Yuhao Zhang. Online Makespan Minimization: The Power of Restart. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We consider the online makespan minimization problem on identical machines. Chen and Vestjens (ORL 1997) show that the largest processing time first (LPT) algorithm is 1.5-competitive. For the special case of two machines, Noga and Seiden (TCS 2001) introduce the SLEEPY algorithm that achieves a competitive ratio of (5 - sqrt{5})/2 ~~ 1.382, matching the lower bound by Chen and Vestjens (ORL 1997). Furthermore, Noga and Seiden note that in many applications one can kill a job and restart it later, and they leave an open problem whether algorithms with restart can obtain better competitive ratios. We resolve this long-standing open problem on the positive end. Our algorithm has a natural rule for killing a processing job: a newly-arrived job replaces the smallest processing job if 1) the new job is larger than other pending jobs, 2) the new job is much larger than the processing one, and 3) the processed portion is small relative to the size of the new job. With appropriate choice of parameters, we show that our algorithm improves the 1.5 competitive ratio for the general case, and the 1.382 competitive ratio for the two-machine case.

Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Online algorithms
  • Online Scheduling
  • Makespan Minimization
  • Identical Machines


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