Why it matters
Christofides is classic algorithm. Understanding shapes approximation.
Advertisement
The architecture
Compute MST.
Match odd-degree vertices (min-weight).
Form Eulerian; shortcut duplicates.
Advertisement
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.