Why it matters

TSP approx enables practical large TSP. Understanding shapes technique selection.

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The architecture

2-approx: build MST, DFS traversal.

Christofides: MST + matching + Eulerian.

TSP 2-approxBuild MSTmin treeDFS traverseshortcut repeats2-approxcost <= 2 * OPTRequires metric TSP (triangle inequality) for approximation guarantees
TSP approx.
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How it works end to end

2-approx: MST weight <= OPT; DFS + shortcut <= 2 * MST.

Better: Christofides.

Local search improvements (2-opt, LKH).