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Metric facility placement planner
Edition: 8 October 2026. Initial decision: Conditional engineering. The product interpretation and pricing are hypotheses; independent proof and buyer validation remain open.
Research finding
The result claims deterministic polynomial-time k-median approximation with factor 1+2/e+epsilon for finite rational metrics and specified facility candidates. It opens at most k facilities; the polynomial may depend on epsilon.
Problem and buyer
An operations team selecting a fixed number of depots or service points needs to reduce aggregate distance and understand how far a proposed plan can be from the best plan under a stated model.
What the finding could enable
A planning tool could produce a candidate plan with a documented model-specific approximation guarantee and scenario comparisons. The theorem strengthens a solver backend; the planner, data cleaning and integrations were already possible.
Technical and commercial limits
Capacity, fixed opening costs, time windows, directed travel times and fairness constraints are not covered automatically. A road-time matrix may violate symmetry or triangle inequalities. The theorem's approximation factor is not an instance-specific optimality certificate.
Minimal architecture
Metric and candidate-site validator -> research approximation backend -> lower-bound baseline -> scenario viewer -> export. Reject unsupported constraints or route them to separately labeled solver modes.
Existing alternatives and differentiation
Commercial optimization suites and tailored location-planning tools are established substitutes. A narrow vertical and trusted data pipeline are more credible differentiation than a generic map UI.
Monetization hypothesis
Hypothesis: AUD 5,000-20,000 per site-planning engagement or an annual vertical subscription after repeat use is established. Contract ranges are prospective assumptions, not observed quotes.
Validation experiment
Compare objective values, constraint fidelity and runtime with exact optima on small cases and established heuristics on larger instances. Measure sensitivity to inaccurate distances and epsilon choices.
Conditions to reject or defer
Defer if the buyer's problem is capacitated or nonmetric, or if existing solvers provide stronger practical solutions within their time budget.
Next concrete action
Review the algorithm's epsilon dependence and build a strict metric-instance validator before any location demo.
Source evidence
Repository sources are pinned to revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Selected scope notes and manuscript statements have been reviewed to the extent described above; these links do not represent successful kernel checks.
Family 125
Subject: The metric <i>k</i>-median approximation threshold and recovery.
- Single-exponential recovery and bounded-price strictness for metric k-median
- The approximation threshold for metric k-median
- Formal scope notes
Current alternative sources
Primary documentation reviewed on 8 October 2026. Product availability demonstrates alternatives, not demand or willingness to pay for this proposal.