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Optimal-order randomized k-server

The online problem compares movement cost with an offline optimum that sees the full sequence.

Progress records 1

Understand the problem ↓

1 record · How we rate progress

Understanding the problem

Read the background

The online problem compares movement cost with an offline optimum that sees the full sequence. Special metrics and larger polylogarithmic upper bounds do not attain the stated general-metric order.

The adversary is oblivious. Repeated initial positions can require a configuration-dependent additive term. The record is separate from deterministic k-server and does not promise an efficient implementation.

Why it matters

If correct, matches the stated general-metric worst-case order for randomized online k-server.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The adversary is oblivious. Repeated initial positions can require a configuration-dependent additive term. The record is separate from deterministic k-server and does not promise an efficient implementation.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

Website timeline

Publication dates and editorial changes.