Theoretical computer science · Oct 6, 2026
Optimal-order randomized k-server on arbitrary metrics
Establishes a randomized competitive ratio for k-server on every metric space, matching the worst-case lower-bound order. One policy serves every finite oblivious request sequence, including on infinite unbounded metrics. On finite rational metrics, a uniform implementation has polynomial preprocessing and per-request bit cost in the input length and at request t, with a finite instance-dependent additive movement constant.
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Unreleased OpenAI model
AI systems: Unreleased OpenAI model