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Online Flexible Busy Time Scheduling on Heterogeneous Machines

Authors Gruia Călinescu, Sami Davies, Samir Khuller, Shirley Zhang

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Author Details

Gruia Călinescu
  • Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA
Sami Davies
  • Department of EECS and the Simons Institute for the Theory of Computing, UC Berkeley, CA, USA
Samir Khuller
  • Computer Science Department, Northwestern University, Evanston, IL, USA
Shirley Zhang
  • Computer Science Department, Harvard University, Cambridge, MA, USA

Funding

Gruia Călinescu’s work was done in part while visiting Northwestern University. Samir Khuller was supported by NSF 2216970 (IDEAL Institute) as well as a gift from Adobe Research. Sami Davies’s work was done in part while at Northwestern University supported in part by an NSF CI Innovation Fellowship. Shirley Zhang was supported by an NSF Graduate Research Fellowship.

Acknowledgements

We would like to thank an anonymous referee for suggesting that our Algorithm 2 can be adapted to jobs of uniform processing time instead of just unit; indeed this was true.

Cite AsGet BibTex

Gruia Călinescu, Sami Davies, Samir Khuller, and Shirley Zhang. Online Flexible Busy Time Scheduling on Heterogeneous Machines. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.37

Abstract

We study the online busy time scheduling model on heterogeneous machines. In our setting, jobs with uniform length arrive online with a deadline that becomes known to the algorithm at the job’s arrival time. An algorithm has access to machines, each with different associated capacities and costs. The goal is to schedule jobs on machines by their deadline, so that the total cost incurred by the scheduling algorithm is minimized. While busy time scheduling has been well-studied, relatively little is known when machines are heterogeneous (i.e., have different costs and capacities), despite this natural theoretical generalization being the most practical model for clients using cloud computing services. We make significant progress in understanding this model by designing an 8-competitive algorithm for the problem on unit-length jobs and provide a lower bound of 2 on the competitive ratio. The lower bound is tight in the setting when jobs form non-nested intervals. Our 8-competitive algorithm generalizes to one with competitive ratio 8(2p-1)/p < 16 when all jobs have uniform length p.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Scheduling algorithms
Keywords
  • Online algorithms
  • Scheduling
  • Competitive analysis

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