Exact Competitive Ratios of Index Rules for Scheduling with Obligatory Testing

Felix Buld

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arXiv · 2610.40554

Exact Competitive Ratios of Index Rules for Scheduling with Obligatory Testing

Felix Buld

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Abstract

We revisit scheduling with obligatory testing, where each job consists of two operations: a test with an initially known time and an operation whose processing time is revealed upon completion of the job's test. We develop an iterative competitive-ratio-preserving instance-reduction method that enables us to compute exact competitive ratios directly on highly structured instances for various index rules. Our main result is a clean analysis showing that the competitive ratio of the algorithm $1$-SORT is exactly the Golden Ratio $φ\approx 1.618$, improving the recent best-known upper bound of $1.861$ for arbitrary testing times. We further leverage this method to obtain near-tight bounds for a simple randomized algorithm on instances with uniform testing times.

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Felix Buld. 2026-10-29. Exact Competitive Ratios of Index Rules for Scheduling with Obligatory Testing. https://arxiv.org/abs/2610.40554

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