Planar metric embedding and flow-cut review

Family 089: Bounded-distortion <i>L</i>₁ embeddings of planar and bounded-treewidth graphs. First review, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Routing researchers can evaluate L1 metric abstractions for planar or bounded-treewidth graph models.

Applicability and commercial boundary

A bounded distortion theorem does not automatically provide a useful constructible embedding or preserve arbitrary operational constraints. Planarity, weights and treewidth must be verified.

Initial business decision

Conditional research. Commercial demand and profitability remain hypotheses.

Next verification action

Review whether the paper gives an effective construction and extract constants and preprocessing requirements.

Evidence scope

The catalog statement was individually reviewed. Main-paper and selected formal-scope passages were additionally inspected for families 090, 093, 094, 097, 325, 328 and 332; this record does not claim a full proof audit or independent Lean verification. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.