Prove UniformKServer (openai/math family 110: Optimal-order randomized $k$-server on arbitrary metrics) in…
Prove UniformKServer (openai/math family 110: Optimal-order randomized $k$-server on arbitrary metrics) in…: a task in openai/math as Harbor environments (Harbor dataset). Context: this statement belongs to family 110 of the release, Optimal-order randomized $k$-server on arbitrary metrics…
The task
Context: this statement belongs to family 110 of the release, *Optimal-order randomized $k$-server on arbitrary metrics* (Theoretical computer science). The family as a whole: Establishes a randomized competitive ratio $O(\log^2(k+1))$ for $k$-server on every metric space, matching the worst-case lower-bound order.…
Part of raising-heart/openai-math.