Why it matters

Christofides is classic algorithm. Understanding shapes approximation.

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The architecture

Compute MST.

Match odd-degree vertices (min-weight).

Form Eulerian; shortcut duplicates.

Christofides flowMSTmin spanning treeMatch odd degreesmin weight matchingEulerian + shortcutfinal tourRecent result improved to 1.5 - epsilon for special cases
Christofides.
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How it works end to end

MST has some odd-degree vertices.

Perfect matching on odd-degree subset.

Union: all even → Eulerian.

Shortcut duplicates → Hamiltonian.