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Lecture 27 APX-Complete

This lecture covers the MAX3SAT theorem, the importance of the PCP system, APX-completeness, L-reductions, and the properties of the APX class. It also includes proofs for the MI-4 and VC-4 problems being APX-complete and an exercise on constructing an L-reduction from MAX3SAT-3 to VC-4.

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Lecture 27 APX-Complete

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  1. Lecture 27APX-Complete

  2. MAX3SAT

  3. Theorem

  4. Theorem This an important result proved using PCP system. Theorem

  5. ClassAPX

  6. L-reduction

  7. VC-b Theorem

  8. 1 2 1 2 v 3 3 4 5 4 5 G G’

  9. Properties (P1) (P2)

  10. APX PTAS

  11. APX-complete Theorem

  12. MAX3SAT-3 Theorem expender

  13. MI-b Theorem

  14. MI-4 is APX-complete Proof. (L1) (L2)

  15. VC-4 is APX-complete Proof. (L1) (L2)

  16. Exercise • Construct a polynomial-time L-reduction from MAX3SAT-3 to VC-4.

  17. Thanks, end.

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