Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs

Authors Enze Sun, Zonghan Yang, Yuhao Zhang

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Author Details

Enze Sun
  • The University of Hong Kong, Hong Kong, China
Zonghan Yang
  • Shanghai Jiao Tong University, China
Yuhao Zhang
  • Shanghai Jiao Tong University, China


The authors would like to thank Minming Li, Pinyan Lu, and Biaoshuai Tao for many insightful discussions on the research topic of this paper.

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Enze Sun, Zonghan Yang, and Yuhao Zhang. Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 97:1-97:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We consider the Online Rent Minimization problem, where online jobs with release times, deadlines, and processing times must be scheduled on machines that can be rented for a fixed length period of T. The objective is to minimize the number of machine rents. This problem generalizes the Online Machine Minimization problem where machines can be rented for an infinite period, and both problems have an asymptotically optimal competitive ratio of O(log(p_max/p_min)) for general processing times, where p_max and p_min are the maximum and minimum processing times respectively. However, for small values of p_max/p_min, a better competitive ratio can be achieved by assuming unit-size jobs. Under this assumption, Devanur et al. (2014) gave an optimal e-competitive algorithm for Online Machine Minimization, and Chen and Zhang (2022) gave a (3e+7) ≈ 15.16-competitive algorithm for Online Rent Minimization. In this paper, we significantly improve the competitive ratio of the Online Rent Minimization problem under unit size to 6, by using a clean oracle-based online algorithm framework.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Online Algorithm
  • Scheduling
  • Machine Minimization
  • Rent Minimization


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