Metric facility placement planner

Family 125: The metric <i>k</i>-median approximation threshold and recovery. First review, 8 October 2026.

Problem and potential new use

Operations teams can evaluate fixed-cardinality facility plans under a valid finite rational metric.

Applicability and commercial boundary

The approximation guarantee does not cover capacities, nonmetric travel costs or an instance-specific optimality certificate.

Initial business decision

Conditional engineering. Buyer demand and profitability remain hypotheses. This first pass does not establish a validated commercial market.

Next verification action

Inspect epsilon-dependent runtime and validate the input metric and candidate set.

Evidence scope

Catalog statement reviewed; inspect linked opportunity dossier for any deeper source review. This record alone does not establish full manuscript or proof verification.

Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata for the exact manuscripts and available scope notes.