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Online Scheduling on Identical Machines with a Metric State Space

Authors Hiromichi Goko, Akitoshi Kawamura, Yasushi Kawase, Kazuhisa Makino, Hanna Sumita

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Author Details

Hiromichi Goko
  • Toyota Motor Corporation, Aichi, Japan
Akitoshi Kawamura
  • Kyoto University, Japan
Yasushi Kawase
  • University of Tokyo, Japan
Kazuhisa Makino
  • Kyoto University, Japan
Hanna Sumita
  • Tokyo Institute of Technology, Japan

Funding

This work was partially supported by the joint project of Kyoto University and Toyota Motor Corporation, titled "Advanced Mathematical Science for Mobility Society", JST PRESTO Grant Number JPMJPR2122, and JSPS KAKENHI Grant Numbers JP17K12646, JP19K22841, JP20H05967, JP20K19739, JP21K17708, and JP21H03397.

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Hiromichi Goko, Akitoshi Kawamura, Yasushi Kawase, Kazuhisa Makino, and Hanna Sumita. Online Scheduling on Identical Machines with a Metric State Space. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 32:1-32:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.STACS.2022.32

Abstract

This paper introduces an online scheduling problem on m identical machines with a metric state space, which generalizes the classical online scheduling problem on identical machines, the online traveling salesman problem, and the online dial-a-ride problem. Each job is associated with a source state, a destination state, a processing time, and a release time. Each machine can process a job on and after its release time. Before processing a job, a machine needs to change its state to the source state (in a time corresponding to the distance), and after the process of the job, the machine’s state becomes the destination state. While related research deals with a model in which only release times are unknown to the algorithm, this paper focuses on a general model in which destination states and processing times are also unknown. The main result of this paper is to propose a O(log m/log log m)-competitive online algorithm for the problem, which is best possible. A key approach is to divide the difficulty of the problem. To cope with unknown release times, we provide frameworks to produce a min{2ρ+1/2, ρ+2}-competitive algorithm using a ρ-competitive algorithm for a basic case where all jobs are released at time 0. Then, focusing on unknown destination states and processing times, we construct an O(log m/log log m)-competitive algorithm for the basic case. We also provide improved algorithms for some special cases.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • Online scheduling
  • Competitive analysis
  • Online dial-a-ride

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References

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