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Online interval scheduling: randomized and multiprocessor cases

Author

Listed:
  • Stanley P. Y. Fung

    (University of Leicester)

  • Chung Keung Poon

    (City University of Hong Kong)

  • Feifeng Zheng

    (Xi’an Jiaotong University)

Abstract

We consider the problem of scheduling a set of equal-length intervals arriving online, where each interval is associated with a weight and the objective is to maximize the total weight of completed intervals. An optimal 4-competitive algorithm has long been known in the deterministic case, but the randomized case remains open. We give the first randomized algorithm for this problem, achieving a competitive ratio of 3.5822. We also prove a randomized lower bound of 4/3, which is an improvement over the previous 5/4 result. Then we show that the techniques can be carried to the deterministic multiprocessor case, giving a 3.5822-competitive 2-processor algorithm, and a 4/3 lower bound for any number of processors. We also give a lower bound of 2 for the case of two processors.

Suggested Citation

  • Stanley P. Y. Fung & Chung Keung Poon & Feifeng Zheng, 2008. "Online interval scheduling: randomized and multiprocessor cases," Journal of Combinatorial Optimization, Springer, vol. 16(3), pages 248-262, October.
    • Handle: RePEc:spr:jcomop:v:16:y:2008:i:3:d:10.1007_s10878-007-9131-z
    DOI: 10.1007/s10878-007-9131-z
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    Cited by:

    1. Ge Yu & Sheldon H. Jacobson, 2020. "Primal-dual analysis for online interval scheduling problems," Journal of Global Optimization, Springer, vol. 77(3), pages 575-602, July.
    2. Meghan Shanks & Ge Yu & Sheldon H. Jacobson, 2023. "Approximation algorithms for stochastic online matching with reusable resources," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 43-56, August.
    3. Nicolas Pinson & Frits C. R. Spieksma, 2019. "Online interval scheduling on two related machines: the power of lookahead," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 224-253, July.
    4. Wenjie Li & Jinjiang Yuan, 2015. "An Improved Online Algorithm for the Online Preemptive Scheduling of Equal-Length Intervals on a Single Machine with Lookahead," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-9, December.

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