Approximation Algorithms for Scheduling Multiple Feasible Interval Jobs

  • Authors:

  • Jian-Jia Chen;Jun Wu;Chi-Sheng Shih;Tei-Wei Kuo

  • Affiliations:

  • National Taiwan University;Chung Kuo Institute of Technology;National Taiwan University;National Taiwan University

  • Venue:
  • RTCSA '05 Proceedings of the 11th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications
  • Year:
  • 2005

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Abstract

Time-critical jobs in many real-time applications have multiple feasible intervals. Such a job is constrained to execute from start to completion in one of its feasible intervals. A job fails if the job remains incomplete at the end of the last feasible interval. This paper is concerned with how to find a schedule in which the number of jobs completed in one of their feasible intervals is maximized. We show that the maximization problem is NP-hard for both non-preemptible and preemptible jobs. This paper develops two approximation algorithms for non-preemptible and preemptible jobs. When jobs are non-preemptible, Algorithm LECF is with a 2-approximation factor; when jobs are preemptible, Algorithm LEF is proved being a 3-approximation algorithm. We also show that our analysis on the two algorithms is tight by providing a set of input instances. Simulation results demonstrate that Algorithms LECF and LEF not only guarantee the approximation factors but also outperform other multiple feasible interval scheduling algorithms.