AI-assisted proof of the deterministic k-server conjecture
Coester, Koutsoupias and Zbysiński report that the work function algorithm is k-competitive on every metric space.
Original report: 2026-09-14The deterministic k-server conjecture
Move k servers through a metric space to serve online requests while competing with an offline optimum.
Progress records 1
Understand the problem ↓1 record · How we rate progress
Understanding the problem
Read the background
Move k servers through a metric space to serve online requests while competing with an offline optimum. Is competitive ratio k attainable on every metric?
Why it matters
A precise target for comparing mathematical claims, their baselines, and the documented contribution of AI.
What counts as progress
A sourced theorem, construction, algorithm, bound, or substantive formalization with its assumptions and AI role stated.
What to watch for
- Check the exact hypotheses and compare with the stated prior baseline.
- Distinguish a source claim, an available proof, and a reproduced verification.
- Retain human contributions, competing work, corrections, and withdrawals.
Background review: 2026-10-11. Selected sources:
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Publication dates and editorial changes.