License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2022.32
URN: urn:nbn:de:0030-drops-158421
Go to the corresponding LIPIcs Volume Portal

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

Online Scheduling on Identical Machines with a Metric State Space

LIPIcs-STACS-2022-32.pdf (0.7 MB)


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.

BibTeX - Entry

  author =	{Goko, Hiromichi and Kawamura, Akitoshi and Kawase, Yasushi and Makino, Kazuhisa and Sumita, Hanna},
  title =	{{Online Scheduling on Identical Machines with a Metric State Space}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{32:1--32:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-158421},
  doi =		{10.4230/LIPIcs.STACS.2022.32},
  annote =	{Keywords: Online scheduling, Competitive analysis, Online dial-a-ride}

Keywords: Online scheduling, Competitive analysis, Online dial-a-ride
Collection: 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)
Issue Date: 2022
Date of publication: 09.03.2022

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI