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Greedy Is Optimal for Online Restricted Assignment and Smart Grid Scheduling for Unit Size Jobs

  • Fu-Hong LiuEmail author
  • Hsiang-Hsuan Liu
  • Prudence W. H. Wong
Conference paper
  • 92 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11926)

Abstract

We study online scheduling of unit-sized jobs in two related problems, namely, restricted assignment problem and smart grid problem. The input to the two problems are in close analogy but the objective functions are different. We show that the greedy algorithm is an optimal online algorithm for both problems. Typically, an online algorithm is proved to be an optimal online algorithm through bounding its competitive ratio and showing a lower bound with matching competitive ratio. However, our analysis does not take this approach. Instead, we prove the optimality without giving the exact bounds on competitive ratio. Roughly speaking, given any online algorithm and a job instance, we show the existence of another job instance for greedy such that (i) the two instances admit the same optimal offline schedule; (ii) the cost of the online algorithm is at least that of the greedy algorithm on the respective job instance. With these properties, we can show that the competitive ratio of the greedy algorithm is the smallest possible.

Keywords

Optimal online algorithm Restricted assignment Smart grid scheduling 

Notes

Acknowledgment

The authors would like to thank Marcin Bienkowski for helpful discussion.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computer ScienceNational Tsing Hua UniversityHsinchuTaiwan
  2. 2.Department Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  3. 3.Institute of Computer ScienceWroclaw UniversityWroclawPoland
  4. 4.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK

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