Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 125-02. The approximation threshold for metric k-median
Manuscript map · lines 4865–4874
OpenAI@2026-10-07#rem:oai-p-125-02
Authors: OpenAI. Family 125.
Title: The approximation threshold for metric k-median.
Abstract: For every fixed ε > 0, we give a deterministic polynomial-time $(1+2/e+{}varepsilon)$-approximation for finite rational metric k-median with specified candidate facilities, opening at most k facilities. Under $P{}ne NP$, the infimum approximation factor in this model is therefore $1+2/e$.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- section: Manuscript map
- remark: Remark: 001-01. Milne's rationality conjecture for abelian varieties
- remark: Remark: 002-01. Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank
- remark: Remark: 002-02. The Selmer converse for elliptic curves at every prime
- remark: Remark: 002-03. The two-primary Birch–Swinnerton-Dyer formula in Selmer corank at most one
- remark: Remark: 003-01. The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane s 7/8
- remark: Remark: 003-02. The Quasi-Riemann Hypothesis (alternate 11/12 proof)
- remark: Remark: 003-03. Uniform exclusion of Landau–Siegel zeros