Lax Lean Archive

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Proof of `Projecting an unweighted approximation gives a weighted approximation`

groundedproofs/Lax263307Proofs/WeightedProjection.lean · lax-263307

What this proof establishes

thm✓Lax263307.WeightedProjection

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

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Description

The projected independent set meets the full weighted approximation guarantee.

Proof strategy

Choose an optimum only for analysis. Its weight is at least the maximum vertex weight, so rounding loses at most an ε/2ε/2 fraction of that optimum. Lift this comparison set and use the unweighted ε/2ε/2 approximation. Projection has weight at least the scale times the number of selected copies. The combined factor (1−ε/2)2(1-ε/2)² is at least 1−ε1-ε.

Attribution

Bonnet–Chang, proof of Theorem 2 in Section 6.