k-server conjecture proven as multiple open CS problems fall in weeks
naval · x · 2026-09-15
A new arXiv paper The k-server conjecture is true proves the k-server conjecture: a deterministic online algorithm can achieve competitive ratio k on every metric space, via the work function algorithm.
The proof uses an algebraic matrix representation of the work function encoding all feasible paths; min/addition in optimal costs map to multiplication/addition of formal expressions, each work function value corresponds to a determinant of k columns, and requests update the representation via change of basis and row replacement. The amortized analysis rests on a potential function over a larger matrix of coordinate pairs.
The buzz follows several open problems falling in quick succession (k-server, Matroid Secretary, Matrix Spencer). Commenters argue we're moving toward a world without open problems, but math lives on: interesting work will shift to discovering new questions and coherent theoretical frameworks.
Related event: Decades-Old k-Server Conjecture Proven on arXiv(3 posts)→
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