Open Research Index

Machine-Checked Christofides 3/2-Approximation and Polyhedral Complexity Barriers for the Traveling Salesperson Problem in Lean 4

Ian McNelly

Palomar Registrypalomar/PALOMAR-2026-10-30-000013Oct 30, 2026cs.DSscore 0

This formalization develops a machine-checked theory of the Traveling Salesperson Problem (TSP) on finite undirected graphs over Fin n in Lean 4 across two principal modules. First, in Christofides.lean (compared against ChallengeChristofides.lean), we formalize the complete Christofides-Serdyukov 3/2-approximation algorithm for Metric TSP: the Minimum Spanning Tree (MST) lower bound (cost(T) = 2/3 on all nontrivial cuts; Yannakakis DFJ slack matrix nonnegativity and conditional Fiorini-Rothvoss PSD extension complexity scaling; and polynomial-time reductions from Hamiltonian Cycle and…

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