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We establish the first theoretical results for scheduling with testing on a single machine and on identical parallel machines to minimize the total weighted completion time in the adversarial model. We present a deterministic algorithm with a competitive ratio of 2.3166 for single-machine scheduling and show that a randomized variant has a competitive ratio of 2.1523. These algorithms, combined with list scheduling, yield competitive ratios of 2.7763 and 2.5110 for identical parallel machine scheduling.

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Scheduling with Testing: Competitive Algorithms for Minimizing the Total Weighted Completion Time in the Adversarial Model

  • 会议论文

  • 发表日期：

    2025年

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  • Felix Buld,
  • Andreas S. Schulz

摘要

We establish the first theoretical results for scheduling with testing on a single machine and on identical parallel machines to minimize the total weighted completion time in the adversarial model. We present a deterministic algorithm with a competitive ratio of 2.3166 for single-machine scheduling and show that a randomized variant has a competitive ratio of 2.1523. These algorithms, combined with list scheduling, yield competitive ratios of 2.7763 and 2.5110 for identical parallel machine scheduling.